### Home > APCALC > Chapter 6 > Lesson 6.5.1 > Problem6-173

6-173.

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

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.

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

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

1. $h(x) =\frac { \operatorname { sin } ^ { - 1 } ( x ) } { \operatorname { cos } ^ { - 1 } ( x ) }$

Be careful. Do not confuse inverse trig functions with reciprocal trig functions.

$\sin^{-1}(x)\neq \frac{1}{\sin(x)}$

$\sin^{−1}\left(x\right)=\arcsin\left(x\right)$

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

1. $k(x) = (x − 3)^{1/2} (x + 1)^3$