Question

How do you differentiate `y=e^-x/x`?

Answer 1

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

Explanation:

You need to use the quotient rule; `d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2`

so, `dy/dx = (xd/dx(e^-x)-e^-xd/dx(x)) / x^2`

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

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

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