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Derivative of xsinx

To find the derivative of
x\sin x
we will need to use the Product Rule, Power Rule on x, and the derivative of \sin x.

By the Product Rule, (fg)'=f'g+g'f.

By the Power Rule, the derivative of x is equal to 1.

The derivative of \sin x is equal to \cos x.

Now, let’s compute the derivative

\dfrac{d}{dx}(x\sin x)=(x)'\sin x + x\cdot\cos x = \boxed{\sin x + x \cos x}