How do you find the fourth derivative of #e^(2x)#?

1 Answer
Andrea S.
Nov 29, 2016

You can use the chain rule to find the first derivative of #e^(2x)# and differentiate iteratively

Explanation:

#(de^(2x))/dx = (de^(2x))/(d(2x)) * (d(2x))/dx = 2e^(2x)#

#(d^((2))e^(2x))/dx^2 =4e^(2x)#

#(d^((3))e^(2x))/dx^3 =8e^(2x)#

#(d^((4))e^(2x))/dx^4 =16e^(2x)#

In general it is easy to see that:

#(d^((n))e^(alpha x))/dx^n =alpha^n e^(alphax)#

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