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Q.
The derivative of $e^{x^3}$ with respect to $log\, x$ is
Continuity and Differentiability
Solution:
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
$\frac{dz}{dx}=\frac{1}{x}$
$\therefore \frac{dy}{dz}=\frac{\frac{dy}{dx}}{\frac{dz}{dx}}$
$=\frac{3x^{2}e^{x^3}}{\left(\frac{1}{x}\right)}$
$=3x^{3}e^{x^3}$