- #1
Specter
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Homework Statement
Differentiate
##F(x)=4^{3x}+e^{2x}##
Homework Equations
The Attempt at a Solution
I have an exam coming up and need some help with this problem.
##F(x)=4^{3x}+e^{2x}##
##f(x)=4^{3x}##
##G(x)=e^{2x}##
First I need to find f'(x) and g'(x), which I thought I did correctly until I found a different answer online.
Following the chain rule for exponential functions in the form ##f(x)=a^{g(x)}##
##f'(x)=a^x(\ln a)(g'(x))##
##f'(x)=4^{3x}(\ln4)(3)##
Following the chain rule for functions in the form of ##f(x)=e^x##
##G'(x)=e^x(\ln e)(g'(x))##
##G'(x)=e^{2x}(2)##
Sum rule:
F'(x)=f'(x)+g'(x)
##=4^{3x}(\ln 4)(3)+(2)e^{2x}##
I think I've messed up somewhere. I'm lost at this point.