Question

How do you differentiate `f(y) = e^y /y`?

Answer 1

`(df)/(dy)=e^y((y-1)/y^2)`

Explanation:

We use quotient rule here. According to quotient rule

if `f(x)=(g(x))/(h(x))`

`(df)/(dx)=(h(x)*g'(x)-g(x)*h'(x))/(h(x))^2`

As `f(y)=e^y/y`

`(df)/(dy)=(yxxe^y-e^yxx1)/y^2`

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