- #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.