How do you differentiate $f (x) = (5 e^{x} + cos x) (x - 2)$ $f(x)=(5e^x+cosx)(x-2)$ using the product rule?

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Answer 1 · 2017-02-10T13:11:58

$= 5 x e^{x} - 5 e^{x} - x sin x + 2 sin x + cos x$ $=5xe^x-5e^x-xsinx+2sinx+cosx$

If $f (x) = g (x) \cdot h (x)$ $f(x)=g(x)*h(x)$ , you know that

$f'(x)=g'(x)*h(x)+g(x)*h'(x)$ (product rule), then

$f'(x)=(5e^x-sinx)(x-2)+(5e^x+cosx)*1$

$=5xe^x-xsinx-10e^x+2sinx+5e^x+cosx$

$=5xe^x-5e^x-xsinx+2sinx+cosx$

How do you differentiate f(x)=(5e^x+cosx)(x-2)f(x)=(5ex+cosx)(x−2)f(x)=(5e^x+cosx)(x-2) using the product rule?