`g(t) = 2/(3t^2)` Use the rules of differentiation to find the derivative of the function.

Textbook Question

Chapter 2, Review - Problem 15 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

Given: `g(t)=2/(3t^2)`

First rewrite the function as `g(t)=(2t^-2)/3`

Find the derivative of the function by using the power rule.

`g'(t)=-2(2/3)t^-3`

`g'(t)=(-4/3)t^-3`

The derivative is `g'(t)=-4/(3t^3)`

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loves2learn's profile pic

loves2learn | (Level 3) Salutatorian

Posted on

Using a Quotient rule:

Given,

Then,

Therefore,

`y'=((0)(3t^2)-(2)(6t))/(3t^2)^2 `

Simplify it all down,

`y'=-4/(3t^3) `

Note that you should get the same answer if you used a product rule. If you don't, then check your answer because you must have made a mistake along the way.

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