### Home > CALC3RD > Chapter Ch5 > Lesson 5.5.2 > Problem5-172

5-172.

Write 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.

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

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

$\text{Recall that }\frac{1}{\text{sin}(x^{2})}=\text{ csc}(x^{2}),\text{ and use the Chain Rule only.}$

3. $f (x) = x \operatorname{tan}(x^2)$

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

4. $g(x)=\cos\left(x\sqrt{x+1}\right)$)

Use the Chain Rule combined with the Product Rule.