What is the derivative of $5^{x^{2}}$ $5^(x^2)$ ?

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Answer 1 · 2017-02-14T02:47:13

$2 ln (5) x 5^{x^{2}}$ $2 ln(5) x 5^(x^2)$

You have to use exponential form :
$5^{x^{2}} = e^{x^{2} ln (5)}$ $5^{x^2} = e^{x^2 ln(5)}$ .

So , you know that the derivative of $e^{u}$ $e^{u}$ is $u' e^{u}$ , therefore, the derivative of $5^(x^2)$ is

$2ln(5) x e^(x^2 ln(5)) = 2ln(5) x 5^(x^2)$ .

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