Write the derivative of each of the following functions.

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

   Hint (a):

   Use the Product Rule.

   Answer (a):

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

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

   Hint (b):

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

3. $f(x)=$ $(2x+1)(3x-1)^3$ 

   Hint (c):

   Combine the Product Rule with the Chain Rule.

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

   Hint (d):

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