Question

The differential of $e^{x^3}$ with respect to $\log x$ is

(A) $e^{x^3}$

(B) $3 x^2 2 e^{x^3}$

(C) $3 x^3 e^{x^3}$

(D) $3 x^2 e^{x^3}+3 x^2$

Answer 1

$\therefore \quad \frac{d y}{d x}=e^{x^3}\left(3 x^2\right)=3 x^2 e^{x^3}$

and $\quad \frac{d z}{d x}=\frac{1}{x}$

$\therefore \quad \frac{d y}{d z}=\frac{d y / d x}{d z / d x}=\frac{3 x^2 e^{x^3}}{(1 / x)}=3 x^3 e^{x^3}$

So, The correct option will be (C).