Differentiate the following functions with respect to x: 3^ x^2+2… - Vidyadip

Question

Differentiate the following functions with respect to x:
$3^{\text{x}^2+2\text{x}}$

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Answer

Consider $\text{y}=3^{\text{x}^2+2\text{x}}$
Differentiate it with respect to x,
$\frac{\text{d}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(3^{\text{x}^2+2\text{x}}\Big)$
$=3^{\text{x}^2+2\text{x}}\times\log3\frac{\text{d}}{\text{dx}}(\text{x}^2+2\text{x})$
[Using chain rule]
$=(2\text{x}+2)\log3\times3^{\text{x}^2+2\text{x}}$
Hence, the solution is, $\frac{\text{d}}{\text{dx}}\big(3\text{x}^2+2\text{x}\big)=(2\text{x}+2)\log3\times3^{\text{x}^2+2\text{x}}$

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