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

1 Answer
Sep 4, 2016

#9 e^(9 x)#

Explanation:

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)#