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If f(x)=xcosx, find f''(x)....

If `f(x)=xcosx`, find `f''(x)`.

Text Solution

Verified by Experts

The correct Answer is:
`x(d)/(dx)(cosx)+cosx(d)/(dx)(x)`
Using the Product Rule, we have
`f'(x)=x(d)/(dx)(cosx)+cosx(d)/(dx)(x)`
`=-xsinx+cosx`
To find `f''(x)` we differentiate f'(x) :
`f''(x)=(d)/(dx)(-xsinx+cosx)`
`=-x(d)/(dx)(sinx)+sinx(d)/(dx)(-x)+(d)/(dx)(cosx)`
`=-xcosx-sinx-sinx=-xcosx-2sinx`
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