Find the indicated derivative. \\ y =\frac{ t^2 + 9}{(2t - 8)^6}

Question:

Find the indicated derivative.

{eq}y =\frac{ t^2 + 9}{(2t - 8)^6} {/eq}

Rules of Differentiation:

There are four rules of differentiation.

1. Power Rule (applies to power functions)

2. Product Rule (applies to product of functions)

3. Quotient Rule (applies to quotient of functions)

4. Chain Rule (applies to composite functions)

The power rule states: {eq}(x^n)' = nx^{n-1} {/eq}

The quotient rule states: {eq}\left( \dfrac f g \right)' = \dfrac{f'g - fg'}{g^2} {/eq}

The chain rule states:

{eq}\left( f(g(x) \right)' = f'(g(x)) \cdot g'(x) {/eq}

We will use these three rules to differentiate this function.

Answer and Explanation:

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We use the quotient rule to differentiate:

{eq}y' = \dfrac{(t^2+9)'(2t-8)^6 - (t^2+9)((2t-8)^6)'}{((2t-8)^6)^2} {/eq}

Now,

{eq}(t^2+9)' =...

See full answer below.


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Differentiation Strategy: Definition & Examples

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Chapter 7 / Lesson 15
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In this lesson, we'll learn about differentiation strategy. We'll define it and look at important characteristics. The lesson will then discuss the pros and cons of differentiation strategy.


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