The differential of {e^{{x^3}}} with respect | vedclass

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Question

(C) Let $y = {e^{{x^3}}}$ and $z = \log x$. To find the derivative of $y$ with respect to $z$,we calculate $\frac{dy}{dz} = \frac{dy/dx}{dz/dx}$. Firs

Vedclass · Accepted Answer

$3{x^3}{e^{{x^3}}}$

Vedclass · Answer

(C) Let $y = {e^{{x^3}}}$ and $z = \log x$. To find the derivative of $y$ with respect to $z$,we calculate $\frac{dy}{dz} = \frac{dy/dx}{dz/dx}$. First,differentiate $y$ with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}({e^{{x^3}}}) = {e^{{x^3}}} \cdot \frac{d}{dx}({x^3}) = 3{x^2}{e^{{x^3}}}$. Next,differentiate $z$ with respect to $x$: $\frac{dz}{dx} = \frac{d}{dx}(\log x) = \frac{1}{x}$. Now,divide the two derivatives: $\frac{dy}{dz} = \frac{3{x^2}{e^{{x^3}}}}{1/x} = 3{x^2} \cdot x \cdot {e^{{x^3}}} = 3{x^3}{e^{{x^3}}}$. Thus,the correct option is $C$.

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

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