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

Question

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

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Answer

Consider $\text{y}=2^{\text{x}^3}$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(2^{\text{x}^3}\Big)$
$=2^{\text{x}^3}\times\log_2\frac{\text{d}}{\text{dx}}(\text{x}^3)$
[Using chain rule]
$=3\text{x}^2\times2^{\text{x}^3}\times\log_2$
Hence, the solution is $\frac{\text{d}}{\text{dx}}\big(2^{\text{x}^3}\big)=3\text{x}^2\times2^{\text{x}^3}\log_2$

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