Find the derivative of the following function: g(x) = (4x^5 + 1)^5.

Question:

Find the derivative of the following function: {eq}g(x) = (4x^5 + 1)^5 {/eq}.

Chain Rule:

The chain rule tells us that the derivative of {eq}f(g(x)) {/eq} is equivalent to {eq}f'(g(x))g'(x) {/eq}.

It essentially tells us that we should derive not only the function outside the smaller function, but also the function inside the larger function.

Answer and Explanation:

We will derive {eq}g(x) = (4x^5 + 1)^5 {/eq} using the chain rule:

{eq}\begin{align*} g(x)& = (4x^5 + 1)^5\\ g'(x)& = 5(4x^5 + 1)^4...

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Using the Chain Rule to Differentiate Complex Functions

from Math 104: Calculus

Chapter 7 / Lesson 6
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