Question

How do you differentiate `y = (x^(2/3) + 3) /( x^(1/5) + x)`?

Answer 1

`y' = (7/15x^(-2/15) -1/3 x^(2/3)-3/5 x^(-4/5) -3)/(x^(1/5)+x)^2`

Explanation:

Use `d/dx(u/v)`=`(v* (du)/dx-u *(dv)/dx)/v^2`

Let `u=x^(2/3)+3`

and `v=x^(1/5)+x`