### Home > CALC3RD > Chapter Ch5 > Lesson 5.5.1 > Problem5-156

5-156.

Write the derivative of each of the following functions.

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

Use the Product Rule.

$f ′(x) = 2x \operatorname{tan}(x) + x^2 \operatorname{sec}^2(x)$

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

Avoid the Quotient Rule! Recall that $\frac{1}{\sin(x)}=\csc(x)$

3. $f (x) = (2x + 1)(3x – 1)^3$

Combine the Product Rule with the Chain Rule.

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

Use the Chain Rule. But, before differentiating, recall that $\sqrt{x+1}=(x+1)^{1/2}.$