Differentiate the following functions with respect to x: 3^ e^ x - Vidyadip

Question

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

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Answer

Let, $\text{y}=3^{\text{e}^{\text{x}}}$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(3^{\text{e}^\text{x}}\Big)$
$=3^{\text{e}^\text{x}}\log3\frac{\text{d}}{\text{dx}}\big(\text{e}^\text{x}\big)$
[Using chain rule]
$=\text{e}^\text{x}\times3^{\text{e}^\text{x}}\log3 $
So,
$\frac{\text{d}}{\text{dx}}\Big(3^{\text{e}^\text{x}}\Big)=\text{e}^\text{x}\times3^{\text{e}^\text{x}}\log3$

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