Answer
a. $\frac{d}{dx}cos^3(x) =-3cos^2(x)sin(x)$
b. $\frac{d}{dx}cos(x^3) =-3x^2sin(x^3)
$
Work Step by Step
Chain Rule:
$\frac{d}{dx}[f(g(x))] = f'(g(x)) \times g'(x)$
a. $y=cos^3(x)$
Outer Function: $y=f(u)=u^3$
Inner Function: $u=g(x)=cos(x)$
$\frac{d}{dx}cos^3(x) = 3cos^2(x) \times -sin(x)$
b. $y=cos(x^3)$
Outer Function: $y=f(u)=cos(u)$
Inner Function: $u=g(x)=x^3$
$\frac{d}{dx}cos(x^3) = -sin(x^3) \times 3x^2$
