Question

How do you find the derivative of `y = x^2e^(-1/x)`?

Answer 1

`dy/dx=(1+2x)e^(-1/x)`.

Explanation:

`y=x^2e^(-1/x)`

By the Product Rule, we get,

`dy/dx=x^2*d/dx(e^(-1/x))+e^(-1/x)*d/dx(x^2)`

`=x^2*e^(-1/x)*d/dx(-1/x)+2x*e^(-1/x)`.......[Chain Rule]

`=x^2*e^(-1/x)*(1/x^2)+2x*e^(-1/x)`

`:. dy/dx=(1+2x)e^(-1/x)`.