# Thread: Derivative using the quotient rule

1. ## Derivative using the product rule

I am familiar with the equation, but I am having trouble working out the entire answer.

"Differentiate using the Product Rule":

h(t)= $\sqrt[3]{t}(t^2+4)$

Thanks!

2. Originally Posted by cynlix
whoops, sorry. I meant product rule.

This is what I have so far...

= $(\frac{1}{3t^\frac{-2}{3}})(t^2+4) + (t^\frac{1}{3}) (1)$ Mr F says: This should either be ${\color{red}(\frac{1}{3t^\frac{2}{3}})(t^2+4) + (t^\frac{1}{3}) (2t)}$ or ${\color{red}(\frac{1}{3} t^\frac{-2}{3})(t^2+4) + (t^\frac{1}{3}) (2t)}$. Everything that followed will be wrong.

[snip]
Putting 1 for the derivative of $t^2 + 4$ was a particularly bad mistake.