Differentiation Using the Limit Definition
Read this topicExplanations 7
- Usage of the limit definition to find derivatives can be a tedious exercise; it requires some complicated algebra. Generally, other techniques of differentiation are preferred, …
By Joshua Siktar, Brian Edwards, Victor Wang, Misha Lavrov, Moor Xu
- When I was young, I had to learn the fundamentals of basketball. You can have all the physical ability in the world, but you still have to know the fundamentals. Michael Jordan …
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- The derivative is usually defined as either ddx(f(x))=limx0→xf(x0)−f(x)x0−x or ddx(f(x))=limΔx→xf(x+Δx)−f(x)Δx\begin{align*} \frac d{dx}(f(x))&=\lim_{x_0\to x}\frac{f(x_0)-f(x…
By Alexander Duan, Ray Li, Alex Federspiel
- Here are some problems to practice Using the Limit Definition of a Derivative. They may be simpler to do using another rule, but the definition is important, so use it! Good luck!
By Freya Edholm
- (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
- (Videos) Limit Definition of Derivative for Rational Functions by PatrickJMT Here's a video by patrickJMT showing you how to use the limit definition of a derivative to find the…
By Alex Federspiel
- (Videos) Limit Definition of Derivative for Square Roots by PatrickJMT Here's a video by patrickJMT where he shows you goes over an example of using the limit definition of a de…
By Alex Federspiel
Problems 4
- If f(x)=x32f(x)=x^{\frac32}f(x)=x23, what is 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)