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