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

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

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Answer 1 · 2016-03-07T16:39:06

#d/(d x) f(x)=(x-2)(2e^x+cos x)+sin x#

Explanation:

#f(x)=(2e^x+sin x)(x-2)#
#d/(d x) f(x)=d/(d x)(2e^x+sin x)(x-2)+d/(d x)(x-2)(2e^x+sin x)#
#d/(d x) f(x)=(2e^x+cos x)(x-2)+(2e^x+sin x)#
#d/(d x) f(x)=2xe^x+x cos x-4e^x-2cos x+2e^x+sin x#
#d/(d x) f(x)=2xe^x-2e^x+x cos x-2cos x+sin x#
#d/(d x) f(x)=2e^x(x-2)+cos x(x-2)+sin x#
#d/(d x) f(x)=(x-2)(2e^x+cos x)+sin x#

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

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