Question

The derivative of $e^{x^3}$ with respect to $logx$ is

• A. $e^{x^3}$
• B. $3x^{2}2e^{x^3}$
• C. $3x^3{e}^{x^3}$
• D. $3x^2{e}^{x^3}+3x^2$

Answer 1

Answer: (C)

Let $y=e^{x^3}$,
$z=logx$
On differentiating $w$.$r$.$t$. $x$, we get
$\frac{dy}{dx}=e^{x^3}\left(3x^2\right)$
$=3x^2{e}^{x^3}$ and
$\frac{dz}{dx}=\frac{1}{x}$
$\therefore \frac{dy}{dz}=\frac{\frac{dy}{dx}}{\frac{dz}{dx}}$
$=\frac{3x^2{e}^{x^3}}{\left(\frac{1}{x}\right)}$
$=3x^3{e}^{x^3}$