How do you differentiate #f(x)=xe^(2x)sinx# using the product rule?

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Answer 1 · 2018-07-22T18:56:27

#f'(x)=e^{2x}(2x\sin x+x\cos x+\sin x)#

Given function:

#f(x)=xe^{2x}\sin x#

differentiating above function using product rule as follows

#d/dxf(x)=d/dx(xe^{2x}\sin x)#

#f'(x)=xe^{2x}d/dx(\sin x)+x\sin xd/dx(e^{2x})+e^{2x}\sin xd/dx(x)#

#=xe^{2x}\cos x+x\sin x(2e^{2x})+e^{2x}\sin x(1)#

#=xe^{2x}\cos x+2xe^{2x}\sin x+e^{2x}\sin x#

#=e^{2x}(2x\sin x+x\cos x+\sin x)#