Question

derive: f(X) cos (1+5x)²

Answer 1

$f(x)=cos(1+5x)^2 \\ f'(x)=cos(1+5x).cos(1+5x) \\ f'(x)=cos(1+5x)'.cos(1+5x)+cos(1+5x).cos(1+5x)' \\ f'(x)=-sen(1+5x).5.cos(1+5x)+cos(1+5x).(-sen(1+5x).5 \\ f'(x)=-5sen(1+5x)cos(1+5x)-5sen(1+5x)cos(1+5x) \\ f'(x)=-10sen(1+5x)cos(1+5x)$
Pode dar uma simplificada ainda mais caso tenha professores exigentes: 
Sabendo que sen(x).cos(x) = 1/2sen(2x)
$f'(x)=-10sen(1+5x)cos(1+5x) = -5sen(2+10x)$