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Question

If f(x)=x cosx, find f′′(x).

A
cosx2 sinx
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B
xcosx2sinx
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C
2xsinx2cosx
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D
xsinx2cosx
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Solution

The correct option is B xcosx2sinx
Using the Product Rule, we have
f(x)=xddx(cosx)+cosxddx(x)
=xsinx+cosx
To find f′′(x), we differentiate f(x) w.r.t x :
f′′(x)=ddx(xsinx+cosx)
=xddx(sinx)+sinxddx(x)+ddx(cosx)
=xcosxsinxsinx=xcosx2sinx

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