# Trigonometric Differentiation Problem.

• Feb 8th 2013, 06:43 AM
KhanDisciple
Trigonometric Differentiation Problem.
Hi, for the life of me I cannot figure this one out.

Find the derivative of $\displaystyle sin^4 \sqrt{u}$.

This is what I tried to do:
$\displaystyle sin^4 \sqrt{u} = (sin\sqrt{u})^4$
$\displaystyle =4(sin\sqrt{u})^3 [cos\sqrt{u}(${\textstyle \frac{1}{2}}u^\frac{-1}{2})]$The answer in the book is$\displaystyle 2\sqrt{u}sin^3 \sqrt{u} cos\sqrt{u}$. How the **** did they get that? Thanks. • Feb 8th 2013, 07:01 AM Plato Re: Trigonometric Differentiation Problem. Quote: Originally Posted by KhanDisciple Hi, for the life of me I cannot figure this one out. Find the derivative of$\displaystyle sin^4 \sqrt{u}$. This is what I tried to do:$\displaystyle sin^4 \sqrt{u} = (sin\sqrt{u})^4\displaystyle =4(sin\sqrt{u})^3 [cos\sqrt{u}({ \frac{1}{2}}u^\frac{-1}{2})]$The answer in the book is$\displaystyle 2\sqrt{u}sin^3 \sqrt{u} cos\sqrt{u}$. How the **** did they get that? Thanks. Note that$\displaystyle 4\sin^3 (\sqrt{u}) \left[cos(\sqrt{u})\left(\frac{1}{2\sqrt{u}}\right) \right]$is the correct answer. Also, because$\displaystyle \sin ~\&~\cos$are functions please use function notation, like$\displaystyle \sin(x) ~\&~\cos(x)\$
• Feb 8th 2013, 07:36 AM
KhanDisciple
Re: Trigonometric Differentiation Problem.
Thank you Plato. The answers appeared completely different to me, and in the future I will try to use the correct notation.