CPM Homework Help : CALC Problem 12-36

Find the derivative for each curve below. (Hint for part (c): Use the natural log function to rewrite this equation.)

$y = \int _ { 3 } ^ { x } \sqrt { 1 + e ^ { u } } d u$
Step (a):
$\frac{d}{dx}y=\frac{d}{dx}\int_3^x\sqrt{1+e^u}du$
Answer (a):
$\frac{dy}{dx}=\sqrt{1+e^x}$

$\left\{ \begin{array} { l } { x ( t ) = \operatorname { cos } 2 t } \\ { y ( t ) = \operatorname { cos } ^ { - 1 } 2 t } \end{array} \right.$
Hint (b):
$\frac{dy}{dx}=\frac{y^\prime(t)}{x^\prime(t)}$