Find the derivative of the function y =  x^2 sin 1/x

To find the derivative of the function y = x^2 sin(1/x), we can use the product rule and the chain rule.

Step 1: Apply the product rule. The product rule states that if we have two functions u(x) and v(x), the derivative of their product is given by (u'v + uv').

Let u(x) = x^2 and v(x) = sin(1/x). Then, u'(x) = 2x and v'(x) = cos(1/x) * (-1/x^2) by the chain rule.

Step 2: Calculate the derivative of y. Using the product rule, we have: y' = (u'v + uv') = (2x * sin(1/x)) + (x^2 * cos(1/x) * (-1/x^2)) = 2x * sin(1/x) - x * cos(1/x)

So, the derivative of the function y = x^2 sin(1/x) is y' = 2x * sin(1/x) - x * cos(1/x).