Find {eq}\;f''(\frac{1}{2})\; {/eq} given {eq}\;f(x) = \ln\left(1 - x\right) {/eq}.


Find {eq}\;f''(\frac{1}{2})\; {/eq} given {eq}\;f(x) = \ln\left(1 - x\right) {/eq}.

Chain Rule for Derivatives

Chain rule is applied to composite functions to get its derivative. The chain rule states that the derivative of the function {eq}f(g(x)) {/eq} is the product of the derivative of the outer function with the derivative of the inner function, that is {eq}\displaystyle \frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x) {/eq}.

Answer and Explanation: 1

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Let's begin by getting the first derivative of the function.

$$\begin{align} f(x) &= \ln\left(1 - x\right) \\ f'(x) &= \frac{d}{dx}\left...

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Using the Chain Rule to Differentiate Complex Functions


Chapter 8 / Lesson 6

Learn how to differentiate a function using the chain rule of differentiation. Find various chain rule derivative examples with various function types.

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