CPM Homework Help : CALC3RD Problem 6-173

Differentiate of each of the following functions. Give answers in factored form where possible.

Hint:

To find the derivative of most of these composite functions, you will need to employ more than one rule: Power Rule, Chain Rule, Product Rule, Quotient Rule, and everything you know about the derivatives of trig functions and exponential functions.

$f(x) =\sqrt { \frac { \operatorname { sin } ( x ) } { \operatorname { tan } ( x ) } }$

$g(x) =e ^ { 1 / ( 1 + x ^ { 2 } ) }$

$h(x) =\frac { \operatorname { sin } ^ { - 1 } ( x ) } { \operatorname { cos } ^ { - 1 } ( x ) }$
Hint (c):
Be careful. Do not confuse inverse trig functions with reciprocal trig functions.
$\sin^{-1}(x)\neq \frac{1}{\sin(x)}$
$\sin^{−1}\left(x\right)=\arcsin\left(x\right)$

$j(x) =( \frac { x ^ { 3 } } { x ^ { 2 } + 5 } )^{-1/3}$

$k(x) = (x − 3)^{1/2} (x + 1)^3$