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Question

if f(x)=x cos x, find f"(x), or d2ydx2


A

- xsinx + cosx

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B

- xcosx - 2sinx

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C

xsinx - cosx

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D

none of these

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Solution

The correct option is B

- xcosx - 2sinx


Using the Product Rule, we have f'(x)=xddx(cos x)+cos xddx(x)=-xsinx+cosx
To find f"(x) we differentiate f'(x):
f"(x)=ddx(-x sin x+cos x)=-xddx(sin x)+sin x ddx(-x)+ddx(cos x)
=-x cos x-sin x-sin x = -x cos x-2 sin x


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