Question

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

Answer 1

`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`