Use a trigonometric identity AFTER you find the derivative.

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

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

Careful!

$\text{arccot}x\neq \frac{1}{\arctan x}$

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