### Home > CALC > Chapter 5 > Lesson 5.5.2 > Problem5-171

5-171.

Find the derivative of each of the following functions.

1. $f(x) = (2x + 1)^2(3x − 1)^3$

Use the Chain Rule combined with the Product Rule.

1. $g ( x ) = \frac { 1 } { \operatorname { sin } ( x ^ { 2 } ) }$

Though you could use the Quotient Rule (combined with the Chain Rule), spare yourself the trouble!

1. $f(x) = x \tan(x^2)$

$f^\prime(x) = \tan(x^2) + 2x^2\sec^2(x^2)$

1. $g ( x ) = \operatorname { cos } ( x \sqrt { x + 1 } )$

Use the Chain Rule combined with the Product Rule.