How do I find the derivative of a function?

Yes, the derivative of a function is used to find the gradient of a graph. dx/dy is the notation used to show that you are finding the derivative (the gradient) of the graph whereas f(x) means 'function of x' and is used to denote the equation of the graph. Hope that helps :)

Hello Fatima. I can answer your questions with great pleasure. Graphs allow us to see what the functions do in a certain range. But the inversion shows us how it changes. They are two different concepts. And also the inverse can be shown in two ways. Derivate’s of the function y=f(x), is y’=f’(x)=dy/dx=d(fx)/dx

The derivative of a function is indeed a new function for the gradient of a graph at a given x-value. You substitute this x-value into the derivative (dy/dx) to find the gradient of the graph at this point. If you then need to find the y-value at this point, which is f(x) i.e the original equation for the graph, you substitute this x-value into the original equation. dy/dx is the derivative function to find the gradient, and f(x) is equal to y, the original function for the graph.

Tushita Gupta Yes, the derivative of a function is used to find the gradient of a graph. dx/dy is the notation used to show that you are finding the derivative (the gradient) of the graph whereas f(x) means 'function of x' and is used to denote the equation of the graph. Hope that helps :)

Hi, I’m Shaunak. In essence, the derivative is a way to calculate the gradient at any point on a graph, if you know the graph’s equation. You may have come across the fact that if you have the graph y = x², the gradient at any point (x,y) on the graph is 2x. If you’ve heard the phrase “first principles”, then that is simply using the definition of the derivative in limit form. That isn’t as scary as it might sound - all it is is your good old change in y over change in x, except the two points are very very very very close together. There should be diagrams on the Internet illustrating this concept. As for your third question, if I interpret this correctly you’re asking about the difference between dy/dx and f’(x)? If that is what you’re asking then the answer is there is no difference - it’s simply different notation. Say you were given the equation y = x². Then dy/dx = 2x. If instead the question phrased the equation as f(x) = x² you would write f’(x) = 2x. I hope that makes sense.

An instantaneous rate of change in the function at a given point is defined as its derivative. At a specific point, the derivative gives a precise slope along the curve. The derivative of the function is represented as dy/dx which means the derivative of y=f(x) with respect to the variable x. Derivative of any function ccan be evaluated using first principal in limit form dy/dx = lim h->0 [f(x+h)-f(x)]/h

Of course! I'd be happy to help you understand calculus concepts. Let's start with your first question. The derivative of a function does indeed help us find the gradient (or slope) of the graph at a particular point (x, y). When we talk about the gradient, we're interested in how steep the graph is at that point. So, the derivative tells us how the function is changing at any given moment. Now, let's move on to your second question about the notation. Don't worry if it seems confusing at first; it takes some time to get used to it. When we write "dy/dx" or "d/dx," we're talking about the derivative of a function y with respect to x. It's a way of saying, "How does y change as x changes?" The "dy" represents a small change in y, and "dx" represents a small change in x. So, "dy/dx" is like saying "the rate of change of y with respect to x." On the other hand, when we have a function written as "f(x) = ..." we're expressing the relationship between the variable x and the corresponding value of the function f. It means that if you plug in a value for x, you can find the value of f(x) using the equation. For example, if we have f(x) = 2x + 3, you can find f(2) by substituting 2 into the equation: f(2) = 2(2) + 3 = 7. Now, when should you use these different functions? Well, "dy/dx" or "d/dx" is used when we want to find the derivative of a function, which helps us understand how it changes. We use this notation when we're talking about slopes or rates of change. On the other hand, the notation f(x) = ... is used when we want to define a function explicitly. It helps us understand how the output (f(x)) relates to the input (x) by using an equation. I hope this explanation helps! Remember, calculus can be challenging at first, but with practice and patience, you'll become more comfortable with these concepts. If you have any more questions, feel free to ask!

Hi Fathima, Yes, finding derivative is a way of finding the gradient at (x, y) dy/dx means the change in y divided by the change in x whereas f(x)= means ‘the function of x’ Use dy/dx for if they ask for the stationary points of a graph for example Use f(x)= to replace y= Use f(x)= for factor theorems for example

dy/dx is the derivative of the function of x with respect to x. While f(x) is the function of x. To solve for the derivative of a function f(x) is dy/dx which can be referred to as the gradient of a linear equation or function. The general formula for solving derivative of a function is as follows: Given that y = Ax^n , then dy/dx = nAx^n-1 . Note that the derivative of a constant is zero

The derivative of a function is a way of finding the gradient of the function, not the gradient of the graph, because the graph does not have a gradient. Dx/Dy is a way of writing out the gradient of the function.

Assalamualaikum Fathima hope uh are doing well.. I can help uh to understand calculus queries so let's start with ur first question derivative of a function is a way of finding the gradient of the function, not the gradient of the graph, because the graph does not have a gradient. Dx/Dy is a way of writing out the gradient of the function.

Yes, you're correct. The derivative of a function at a point (x, y) on a graph gives us the gradient (or slope) of the graph at that point. "dxdy" is a way to denote a derivative in calculus. It tells you how much y changes for a small change in x. "f(x) = ..." is a general way to write any function. It tells you what y equals when you plug in a certain x. Use "dxdy" when you want to find the rate of change or slope at a particular point, and use "f(x) = ..." to calculate the y-value for a given x-value in a function.

Dydx is just the term for the gradient function Fx is the original function(the original equation) Then using differentiation (which is dydx) you end up with the gradient function

To find the derivative of a function firstly you have to know the type of function either it is algebraic, trigonometric, hyperbolic or inverse functions Then you take one dependent variable and differentiate the remaining independent variables

First derivative means the rate of change of that function. There is a formula to find the derivate i.e. f^'(x)=\lim\below{h\rightarrow0}{\frac{f(x+h)-f(x)}{h}}.

I teach you derivation very effectively

The derivative of a function lets us calculate the gradient of a function at any point on the curve. dy/dx and f'(x) are equivalent notations and indicate the function of the derivative.

A function shows how something depends on another thing. Normally we have something like y=x^2 If y represents height and x represents width it tells us that if you move to a specific position on width, you will have a height that is "square more". You could do it the other way and take the square root out of y, that is √y=x and this will give you the same proportion. But now instead saying that if you have a specific height, the width will only be the "square root as much" of that height. All a function does, is that it tells you what proportions you have between different things. It puts it all together for scale. So now, what a derivative does is that it answers a question. A question that is: If I, in say the equation y=x^2 change the width just a tiny tiny bit, how much in comparison will the height change proportionally? If we from the start had f(x)=3x the derivative would be f′(x)=3 . It would tell us that height always increases 3 times as much as the width we have. If we from the start had f(x)=x^2 the derivative is f′(x)=2x . This tells us that height will increase by 2 times as much at the position you are currently at. So the further along the x-axis you are the more a change you will do.

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Hello there! Let's dive into the exciting world of calculus and demystify derivatives for you. The derivative of a function is indeed a way to find the graph's gradient at a specific point (x, y). Think of it as a tool that helps us understand how the graph changes and how steep or flat it is at any given spot. When you find the derivative of a function, you're figuring out its slope or gradient at different points along the graph. Now, let's talk about the difference between dxdy and f(x) = ... The notation "dxdy" is often used to represent the general concept of finding the derivative. It's like a reminder that we want to know how y (the dependent variable) changes concerning x (the independent variable). On the other hand, "f(x) = ..." is a specific way to represent a function. The "f" stands for the name of the function, and "x" is the input or independent variable. The part after the equals sign tells us how the output (usually represented by "y") depends on the input "x." It's like a recipe that tells us how to get the y-values from the x-values. When you want to find the derivative of a function represented as "f(x) = ...," you'll use some rules and formulas that mathematicians have developed to make this process easier. This is where "dxdy" comes into play! It's a way to say, "Hey, let's find the rate of change (derivative) of y with respect to x." So, when should you use the different functions? Well, "f(x) = ..." is for showing the relationship between the input (x) and output (y) of the function, like an instruction manual for your function. On the other hand, "dxdy" is used when you want to find the derivative of that function, which will tell you how quickly y is changing concerning x. Remember, as you continue with calculus, you'll get more familiar with these terms and concepts. It's okay to feel overwhelmed at first, but don't worry! With practice and patience, you'll become a pro at finding derivatives and exploring the amazing world of calculus. Keep exploring and having fun with maths!

In first principle of differentiation: you would first make whatever f(x) is and make it f(x+h) and then use the formula for the first principle of differentiation where h goes to 0. Or you could just multiply the coefficient by the power and take one away from the original power.

Dx mean differential with respect to x. And dy mean differential w r t y

It is a normal feeling to sometimes be overwhelmed especially when confronted with the unfamiliarity. Understanding math concepts sometimes can be intimidating but is summonable with the right approach, commitment and with the right assistance. To answer your first question; yes, the derivative of a function in the form of a curve or graph is the same as finding its gradient. Also, dydx is the term used for the first order derivative of a function. f(x) on the other hand, represents a function. So using them is pretty simple; f(x) is used when you are referring to a function whilst dydx is used when you are referring to a derivative or a first order differential. Hope the response helps...

Finding the derivative of a function depends on the nature of the function. For polynomials in a single variable you multiply each term involving the variable by its power and then reduce the power by 1. So the derivative of 3x^2 +4x - 2 is 6x + 4 (the constant term -2 disappears). For the circular functions cos x is the derivative of sin x, - sin x is that of cos x and tan x differentiates to (sec x)^2. e^x is nice and easy as it is its own derivative and derivatives of the hyperbolic functions (sinh x, cosh x and tanh x) follow a similar pattern to the circular functions. These are general categories of functions and I’ve cited some simple examples. For more complex functions there are specific rules for finding derivatives of products, quotients, functions of functions, multi variable functions, etc. Integration is the opposite process to differentiation and is even more problematic!

Finding the derivative of a function is an essential concept in calculus. The derivative represents the rate at which the function changes with respect to its independent variable. In simple terms, it gives you the slope of the function at any given point. There are several methods to find derivatives, but the most common one is using differentiation rules. Here's a step-by-step guide on how to find the derivative of a function: Step 1: Identify the Function Let's say you have a function, f(x), and you want to find its derivative, denoted as f'(x) or dy/dx. Step 2: Apply Differentiation Rules Use the following rules to differentiate various types of functions: Power Rule: For any constant n, the derivative of x^n is nx^(n-1). Constant Rule: The derivative of a constant (like 3 or 5) is zero. Sum/Difference Rule: The derivative of the sum (or difference) of two functions is the sum (or difference) of their derivatives. Product Rule: The derivative of the product of two functions u(x) and v(x) is u'(x)v(x) + u(x)v'(x). Quotient Rule: The derivative of the quotient of two functions u(x) and v(x) is [u'(x)v(x) - u(x)v'(x)] / v(x)^2. Chain Rule: The derivative of a composite function f(g(x)) is f'(g(x)) * g'(x). Step 3: Simplify After applying the differentiation rules, simplify the expression as much as possible. Example 1: Let's find the derivative of the function f(x) = 3x^2 + 2x - 5. Step 1: The function is f(x) = 3x^2 + 2x - 5. Step 2: Apply the power rule: The derivative of 3x^2 is 2 * 3x^(2-1) = 6x, and the derivative of 2x is 2. Step 3: The derivative of f(x) is f'(x) = 6x + 2. Example 2: Find the derivative of the function g(x) = (2x^3 - 4x^2 + 5) / (x^2). Step 1: The function is g(x) = (2x^3 - 4x^2 + 5) / (x^2). Step 2: Apply the quotient rule: The derivative of 2x^3 is 3 * 2x^(3-1) = 6x^2, the derivative of -4x^2 is 2 * -4x^(2-1) = -8x, and the derivative of 5 is 0. Step 3: The derivative of g(x) is g'(x) = (6x^2 - 8x) / x^2. Remember, practice makes perfect! Keep practicing with different functions to become more comfortable with finding derivatives.

Yes that is correct a derivative of a function is the gradient at a specific point coordinates (x,y). Say a function y =f(x) then the derivative is found by differentiating it such as dy/dx also sometimes f’(x) and gives you the slope at that point.

1. You bring the power and multiply the coefficent together 2. You take the power away by 1

Let's take an example of a function f(x)=x , Now derivative of a function f'(x)=1. If f is a function in (x,y)as f(x,y)=x+y Derivative of a function f'(x,y) =d(f(x,y))/dx=1 f'(x,y)=d(f(x,y))/dy=1. So the partial derivative of a function with several variables is its derivative with respect to one of those variables while other remains as constant.In the example f'(x,y) with respect to x ,y is constant hence we can take its derivative as 0 and x derivative as 1.vice versa with respect to y.

hello, exciting and interesting question. welcome to one of the main core topics of mathematics. A function say f(x) or g(y) etc is a mathematical method of solving a problems. Problems can be solved algebraically or visualize and solve them graphically. Now for your first question :The derivative of a function indeed help us find the slope or gradient of the graph at a particular point (x, y) of course in cartesian coordinates. in real-life, we talk about the gradient, we're interested in how steep the graph is at that point e.g when you ascend a hill. So, the derivative tells us how the function is changing at any given moment or at different points along the curve or line or spots on the hill. For the second question if i'm not mistaken you want the difference between f'(x) and dy/dx? if this is the case , then they mean practically the same thing just different connotations. e.g let's say you are given a function, f(x) = ax + b. a) find f'(x) b) find dy/dx c) df(x)/dx a &c mean same thing in you are asked to find the derivative of f(x) with respect to x which is a. another person could still say let f(x) = y this implies that y = ax + b and corresponds to b and the answer is dy/dx = a NB: it could still be with respect to another variable ok i hope this helps you out. Thanks

The derivative of a function is the slope or steepness of the function. The steepness of a function at any point x=c is the gradient of the tangent at that point.

Derivative means that by small small part the function is being subtracted. For more info contact me

To find the derivative of a function, you can follow these general steps: 1. Identify the function: Let's say the function is denoted as f(x). 2. Use the appropriate derivative rules: Different types of functions have specific rules for finding their derivatives. Here are some common rules: - Power Rule: If the function is in the form f(x) = x^n, the derivative is f'(x) = nx^(n-1). - Sum/Difference Rule: If you have a function in the form f(x) = g(x) + h(x) or f(x) = g(x) - h(x), the derivative is f'(x) = g'(x) + h'(x) or f'(x) = g'(x) - h'(x), respectively. - Product Rule: If the function is in the form f(x) = g(x) * h(x), the derivative is f'(x) = g'(x) * h(x) + g(x) * h'(x). - Quotient Rule: If you have a function in the form f(x) = g(x) / h(x), the derivative is f'(x) = [g'(x) * h(x) - g(x) * h'(x)] / [h(x)]^2. 3. Apply the chain rule: If you have a composition of functions (f o g), use the chain rule to find the derivative. The chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) * h'(x). 4. Simplify: After applying the appropriate derivative rules, simplify the expression to get the final derivative.

With the help of simple polynomial graphs, you can easily identify the difference in the gradients. dxdy means when we take a derivate of a bivariate function in which two variables are involved. While f(x), is a function of x. It depends on the function. If f(x) then we mostly use 'f(x).

there are few rules you must know such as: d(const)/dx=0 dx/dx=1 dx^2/dx=2x and so on

Yes, finding the derivative of a function means you are finding the gradient of that function. If y = x^2 is your function, then the derivative would be F(y) = 2x Now, F(y) will give you the gradient at any point x. At x=3, y=3^2=9 and F(y) = 2*3 =6

Assalamu Alaikum Fathima, Since, You are very new to this topic initially it will be difficult to understand the topic and the different terminologies used in it. You are facing problems in understanding derivatives because you are focusing in understanding certain topics only rather than having in-depth knowledge. Believe me , it won't work like that way. Try to understand the topics like relation, function (in the topic Sets), then limits and continuity first. only after that go for derivatives and Integration. Mark my words, after understanding the concept of continuity it will be easier for you to understand derivatives and its practical applications. Calculus is broadly used in solving problems from Physics, specially in Mechanics and electronics (like how to calculate instantaneous velocity, instantaneous acceleration etc.). So, without thorough knowledge about the topic it will be difficult for you to solve those problems. Coming to your questions : Yes, the derivative of a function of a graph is a way of finding the graph’s gradient at (x, y). d/dx is the symbol used for derivation. dy/dx is used to find the derivative of y with respect to x ( in general words " how the value of y will change when the value of x will change negligibly or in a very small amount). On the other hand F(x) is a function. Suppose, Y=F(x)=2x^3+5 is the function then dy/dx will be the derivative of Y (or F(x)) with respect to "x". (i.e. change in F(x) when the value of x changes very small).

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