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Find the derivative. g(x) = \cos x^6

Question:

Find the derivative. {eq}g(x) = \cos x^6 {/eq}

Derivative of Function:

We have to find the derivative of the given function. It looks like a composite function of x so, when we will take derivative of the composite function using chain rule of differentiation. Use it to get the desired result.

Answer and Explanation:

Using chain rule of differentiation we have $$\begin{align*} g\left( x \right) &= \cos \left( {{x^6}} \right)\\ \frac{d}{{dx}}\left[ {g\left( x \right)} \right] &= \frac{d}{{dx}}\left[ {\cos \left( {{x^6}} \right)} \right]\\ g'\left( x \right) &= - \sin \left( {{x^6}} \right) \cdot \frac{d}{{dx}}\left[ {{x^6}} \right]\\ g'\left( x \right) &= - \sin \left( {{x^6}} \right) \cdot 6{x^5}\\ g'\left( x \right) &= - 6{x^5}\sin \left( {{x^6}} \right). \end{align*} $$


Learn more about this topic:

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Derivatives: The Formal Definition

from Math 104: Calculus

Chapter 7 / Lesson 5
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