### Home > CALC > Chapter 6 > Lesson 6.3.2 > Problem6-93

6-93.

Find the following derivatives. Consider trigonometric substitutions to make your work easier.

1. $\frac { d } { d x } ( 4 \operatorname { cos } 2 x \operatorname { sin } 2 x )$

Use a trigonometric identity AFTER you find the derivative.

4cos(2x)sin(2x) =
2sin(4x)

2. $\frac { d } { d x } ( 6 \operatorname { cos } ^ { 2 } x + 6 \operatorname { sin } ^ { 2 } x )$

Simplify the expression using a trigonometric identity BEFORE you take the derivative.

3. $\frac { d } { d x } \operatorname { arccot } ( 2 ^ { 3 x } )$

Careful!
$\text{arccot}x\neq \frac{1}{\arctan x}$
$\text{arccot}x=\text{arctan}\left (\frac{1}{x} \right )$