`h(x) = 8/(5x^4)` Use the rules of differentiation to find the derivative of the function.

Textbook Question

Chapter 2, Review - Problem 16 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

Find the derivative of `h(x)=(8)/(5x^4)`

First rewrite the function as `h(x)=(8x^-4)/(5)`

then find the derivative of the function using the power rule.

`h'(x)=(-4)(8/5)x^-5` 

The derivative is: `h'(x)=-32/(5x^5)`

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loves2learn's profile pic

loves2learn | (Level 3) Salutatorian

Posted on

Using a quotient rule:

Given,

`y=a/b `

Then,

`y'=((a')(b)-(a)(b'))/b^2 `

Therefore,

`y'=((0)(5x^4)-(8)(20x^3))/(5x^4)^2 `

Simplifying,

`y'=(-160x^3)/(25x^8) `

`y'=-32/(5x^5) `

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