# `g(t) = t^2 - 4/(t^3)` Find the derivative of the function.

### Textbook Question

Chapter 2, 2.2 - Problem 41 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

kalau | (Level 2) Adjunct Educator

Posted on

We can rewrite g(t) so that we can avoid the quotient rule altogether.

`g(t)=t^2-4t^-3`

Use the power rule to derive g(t).  The power rule is:

`d/dx x^n = nx^(n-1)`

`g'(t)= 2t +12 t^-4`

The answer is then:  `g'(t)=2t + 12/t^4`

loves2learn | (Level 3) Salutatorian

Posted on

Although you can avoid the quotient rule, I still think that it is beneficial to practice using it.

Given,

`y=a/b `

Then,

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

Note that this only applies to the second term, as we can apply the Power Rule on the first term.

Therefore,

`g'(t)=2t-((0)(t^3)-(4)(3t^2))/t^6 `

Simplifying it completely, you get

`g'(t)=2t+12/t^4 `

Note that you should get the same answer if you bring the `t^3 ` up top and apply the power rule for both terms. If you don't, then check your work because you probably made a mistake along the way!