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)#