What is the derivative of $e^(9x)$ ?

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Answer 1 · 2016-09-04T16:39:47

$9 e^(9 x)$

We have: $e^(9 x)$

This expression can be differentiated using the "chain rule".

Let $u = 9 x => u' = 9$ and $v = e^(u) => v' = e^(u)$ :

$=> (d) / (dx) (e^(9 x)) = 9 cdot e^(u)$

$=> (d) / (dx) (e^(9 x)) = 9 e ^(u)$

We can now replace $u$ with $9 x$ :

$=> (d) / (dx) (e^(9 x)) = 9 e^(9 x)$

What is the derivative of e^(9x)e^(9x)?