Question

How do you differentiate `y=e^x/x^2`?

Answer 1

The answer is `=(e^x(x-2))/x^3`

Explanation:

We use the derivative of a quotient

`(u/v)'=(u'v-uv')/(v^2)`

`u=e^x`, `=>`, `u'=e^x`

`v=x^2`, `=>`, `v'=2x`

So, `dy/dx=(e^x*x^2-e^x*2x)/(x^4)`

`=(xe^x(x-2))/(x^4)=(e^x(x-2))/x^3`