Find the derivative of the y=xsinx

To find the derivative of the function y = xsinx, we will use the product rule. The product rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.

Let's denote: f(x) = x and g(x) = sinx

The derivative of f(x) is f'(x) = 1 and the derivative of g(x) is g'(x) = cosx.

Applying the product rule, we get:

y' = f'(x)g(x) + f(x)g'(x) y' = 1sinx + xcosx y' = sinx + xcosx

So, the derivative of y = xsinx is y' = sinx + xcosx.