Find the derivative of y = xsinx

To find the derivative of y = xsinx, we can use the product rule.

Let u = x and v = sinx.

Using the product rule, the derivative of y = uv is given by:

dy/dx = u * dv/dx + v * du/dx

In this case, u = x and v = sinx.

Taking the derivative of u = x with respect to x, we get du/dx = 1.

Taking the derivative of v = sinx with respect to x, we get dv/dx = cosx.

Substituting these values into the product rule, we have:

dy/dx = x * cosx + sinx * 1

Simplifying, we get:

dy/dx = x * cosx + sinx

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