### Home > CALC > Chapter 6 > Lesson 6.5.1 > Problem6-174

6-174.

Find the derivatives 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 shortcut: 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. $h ( x ) = \frac { \operatorname { sin } ^ { - 1 } x } { \operatorname { cos } ^ { - 1 } x }$

Careful.
Don't confuse inverse trig with reciprocal trig functions.
$\operatorname{sin}^{-1}x =\operatorname{arcsin}x$

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

1. $k(x) = (x − 3)^{1/2}(x + 1)^3$