Question

How do you find the derivative of `e^(4x)/x`?

Answer 1

`(df)/(dx)=e^(4x)/x^2(4x-1)`

Explanation:

We can use quotient rule, which states that

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

then `(df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2`

Here we have `f(x)=e^(4x)/x`, where `g(x)=e^(4x)` and `h(x)=x`

and therefore `(df)/(dx)=(4e^(4x)xx x-1xxe^(4x))/x^2`

= `e^(4x)/x^2(4x-1)`