Differentiate the following with respect to x | vedclass

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(A) Let $y = e^{x^{3}}$.To differentiate $y$ with respect to $x$,we use the chain rule.$\frac{dy}{dx} = \frac{d}{dx}(e^{x^{3}})$.Applying the chain ru

Vedclass · Accepted Answer

$3x^{2}e^{x^{3}}$

Vedclass · Answer

(A) Let $y = e^{x^{3}}$.To differentiate $y$ with respect to $x$,we use the chain rule.$\frac{dy}{dx} = \frac{d}{dx}(e^{x^{3}})$.Applying the chain rule,we treat $x^{3}$ as a function $u$,so $\frac{d}{dx}(e^{u}) = e^{u} \cdot \frac{du}{dx}$.$\frac{dy}{dx} = e^{x^{3}} \cdot \frac{d}{dx}(x^{3})$.Since $\frac{d}{dx}(x^{3}) = 3x^{2}$,we get:$\frac{dy}{dx} = e^{x^{3}} \cdot 3x^{2} = 3x^{2}e^{x^{3}}$.

Differentiate the following with respect to $x$: $e^{x^{3}}$

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