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

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Answer 1 · 2016-11-06T00:27:56

$d/dx5^(x^2) = (2ln 5)x5^(x^2)$

Let $y = 5^(x^2)$

Take Natural logs of both sides
$ln y = ln 5^(x^2)$
$:. ln y = x^2ln 5$

Differentiate (implicitly) wrt $x$ :
$:. 1/ydy/dx = 2xln 5$
$:. dy/dx = (2ln 5)xy$
$:. dy/dx = (2ln 5)x5^(x^2)$

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