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1. Find the derivative of the function, and evaluate it at x = 1 (radian). Round your answer to...

Question:

1. Find the derivative of the function, and evaluate it at {eq}x = 1 {/eq} (radian). Round your answer to the nearest hundredth.

{eq}y = \tan(9x^2 - 7x + 3) {/eq}

2. Use the Chain Rule to find the derivative, then evaluate it at {eq}x = 1 {/eq} .

{eq}y = (4x^2 - 9x)^3 {/eq}

Chain Rule:

The chain rule is a rule among the set of rules of derivatives. It is used to find the derivative of a function where one function is inside the other. It is used to find the derivative of a composite function. It states:

{eq}\dfrac{d}{dx} (f(g(x)) = f'(g(x)) \cdot g'(x) {/eq}

Answer and Explanation: 1

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(1) The given function is,

{eq}y = \tan(9x^2 - 7x + 3) {/eq}

Here one function is inside the other. So we apply the chain rule to find the...

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Using the Chain Rule to Differentiate Complex Functions

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Chapter 8 / Lesson 6
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If you've ever seen a complicated function, this lesson is for you. Most functions that we want to differentiate are complicated functions, for which no single derivative rule will work. In this lesson, learn how to use the chain rule to simplify nesting equations.


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