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B
−xcosx−2sinx
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C
−2xsinx−2cosx
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D
−xsinx−2cosx
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Solution
The correct option is B−xcosx−2sinx 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) =−xcosx−sinx−sinx=−xcosx−2sinx