CPM Homework Help : CALC Problem 6-174

Find the derivatives 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 shortcut: 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):
Careful.
Don't confuse inverse trig with reciprocal trig functions.
$\operatorname{sin}^{-1}x =\operatorname{arcsin}x$

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

$k(x) = (x − 3)^{1/2}(x + 1)^3$