Hoe do you differentiate #f(x)=ln(e^(4x)+3x) #?

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Answer 1 · 2015-11-09T10:29:54

#f'(x)=frac{4e^{4x}+3}{e^{4x}+3x}#

Let #u=e^{4x}+3x#.

#frac{du}{dx}=4e^{4x}+3#

#f'(x)=frac{d}{dx}[ln(e^{4x}+3x)]#

#=frac{d}{dx}[ln(u)]#

#=frac{d}{du}[ln(u)]frac{du}{dx}#

#=(1/u)(4e^{4x}+3)#

#=frac{4e^{4x}+3}{e^{4x}+3x}#