Derivative as a Function (f')
Read this topicExplanations 6
- In Misha's words: "we've already defined the derivative at a point xxx, and now we define a function called f′(x)f'(x)f′(x) whose value at xxx is that derivative." When we speak…
By Calvin Lee
- Over here, we found the derivative of f(x)=x2f(x)=x^2f(x)=x2 at x=1.x=1.x=1. But we could easily have done the same for x=0,x=0,x=0, x=−1,x=-1,x=−1, x=π,x=\pi,x=π, or x=your fav…
By Ray Li, Po-Shen Loh, Victor Wang
- A derivative tells us how a function changes with respect to an independent variable. In other words, f'(x) is representing the rate of change of f(x). For example, if we look a…
By Emma, Victor Wang
- (Video) Understanding the Definition of Derivative by PatrickJMT Here's a video by patrickJMT explaining derivatives and understanding their definition. The definition of a deri…
By Alex Federspiel
- (Videos) Finding a Derivative Using the Definition of Derivative by PatrickJMT In this video by patrickJMT he shows you how to use the derivative definition to find the derivati…
By Alex Federspiel
- (Video) Calculus - Understanding the derivative as a function by MySecretMathTutor
By Victor Wang
Problems 7
- If f(x)=x32f(x)=x^{\frac32}f(x)=x23, what is f′(x)f'(x)f′(x)?
- If f(x)=x2.687f(x)=x^{2.687}f(x)=x2.687, what is f′(x)f'(x)f′(x)?
- If f(x)=xaf(x)=x^af(x)=xa and a∈Ra\in\mathbb{R}a∈R then find the derivative function f′(x)f'(x)f′(x).
- Find the derivative of the function using the definition of derivative. f(x)=x+xf(x)=x+\sqrt{x}f(x)=x+x
- Find the derivative of the function using the definition of derivative. f(x)=2−x2+xf(x)=\frac{2-x}{2+x}f(x)=2+x2−x
- Find the derivative of the function using the definition of derivative. f(x)=ln(x)f(x)=\ln(x)f(x)=ln(x)
- What is the derivative of f(x)=x23f(x) = x^{\frac{2}{3}}f(x)=x32.