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

Expert Answers
kalau eNotes educator| Certified Educator

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


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 | Student

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


`y=a/b `


`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.


`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!