How do I find the derivative of # f(x)=e^(2x)#?

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Answer 1 · 2016-01-21T23:51:36

#f'(x)=2*e^(2x)#

#f(x)=e^g(x)#

You can use the Chain Rule:

#f'(x)=e^g(x)*g'(x)#

#:.f'(x)=e^(2x)*2=2*e^(2x)#

you can also write:

#f(x)=e^(2x)=(e^x)^2#

#f(x)=[g(x)]^n#

#f'(x)=n[g(x)]^(n-1)*g'(x)#

#f'(x)=2(e^x)^1*e^x#

remembering that: #a^n*a^m=a^(n+m)#

#f'(x)=2e^(x+x)=e^(2x)#