`y = xcos(x) - sin(x)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

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sciencesolve eNotes educator| Certified Educator

You need to evaluate the derivative of the given function, using the product rule for the product x*cos x, such that:

`f'(x) = ((x)'(cos x) + (x)(cos x)') - (sin x)'`

`f'(x) = 1*cos x + x*(-sin x) - cos x`

Reducing like terms yields:

`f'(x) = - x*(sin x)`

Hence, evaluating the derivative of the function, using the product rule, yields `f'(x) = - x*(sin x).`