Question

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

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

Answer 1

The correct option is C $3x^3{e}^{x^3}$

let $f=e^{\left(x^3\right)}$ and $g=logx$

Derivatives are

$\frac{d}{dx}\left(f\right)=\frac{d}{dx}\left(e^{\left(x^3\right)}\right)=3x^2.e^{\left(x^3\right)}\frac{d}{dx}\left(g\right)=\frac{d}{dx}\left(logx\right)=\frac{1}{x}$

Derivative of 'f' w.r.t 'g' is

$\frac{df}{dg}=\frac{\left(\frac{df}{dx}\right)}{\left(\frac{dg}{dx}\right)}=\frac{3x^2\ast e^{x^3}}{\left(\frac{1}{x}\right)}=3x^3{e}^{x^3}$