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  3. ZuAI AP College Board Maths 2020
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Definition of Differentiation

Sarah Miller

Sarah Miller

6 min read

Next Topic - Estimating the Derivative at a Point
Study Guide Overview

This study guide covers the concept of derivatives and their relationship to tangents. It explains how to find the derivative of a function, how it relates to the instantaneous rate of change and the slope of the tangent line. It also covers finding the equation of a tangent line, and identifying horizontal and vertical tangents.

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Previous Topic - Instantaneous Rate of ChangeNext Topic - Estimating the Derivative at a Point

Question 1 of 9

Which of the following represents the limit definition of the derivative of a function f(x)f(x)f(x)? 🤔

f′(x)=lim⁡h→0f(x)−f(x+h)hf'(x) = \lim_{h \to 0} \frac{f(x) - f(x+h)}{h}f′(x)=limh→0​hf(x)−f(x+h)​

f′(x)=lim⁡h→0f(x+h)−f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}f′(x)=limh→0​hf(x+h)−f(x)​

f′(x)=lim⁡h→∞f(x+h)−f(x)hf'(x) = \lim_{h \to \infty} \frac{f(x+h) - f(x)}{h}f′(x)=limh→∞​hf(x+h)−f(x)​

f′(x)=lim⁡h→0f(x+h)+f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h) + f(x)}{h}f′(x)=limh→0​hf(x+h)+f(x)​