Question

What is the derivative of this function `x^(2)sin(1/x)`?

Answer 1

`2xsin(1/x)-cos(1/x)`

Explanation:

Use the product rule: `d/dx(uv)=u'v+uv'` to get

`d/dx(x^2sin(1/x)) = [2x][sin(1/x)]+[x^2][cos(1/x)*(-1/x^2)]`

`= 2xsin(1/x)-cos(1/x)`

For all reals except `0`.