Given f(x) = \cos(\sin(x^2)) , find f'(x) and f'(1)

Question:

Given {eq}f(x) = \cos(\sin(x^2)) {/eq}, find {eq}f'(x) \enspace and \enspace f'(1) {/eq}

Derivatives:

We have a function which is a cosine of a sine function. We will use the chain rule for differentiation in this question as done in the solution. The chain rule is:

{eq}f(g(x))=f'(g(x))g'(x) {/eq}

Answer and Explanation:

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Derivatives: The Formal Definition

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Chapter 7 / Lesson 5

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The derivative in calculus is the rate of change of a function. In this lesson, explore this definition in greater depth and learn how to write derivatives.

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Given {eq}f(x) = \cos(\sin(x^2)) {/eq}, find {eq}f'(x) \enspace and \enspace f'(1) {/eq}

Question:

Derivatives:

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