Question

How do you find the derivative of `y= x/sqrt(x^2+1)` ?

Answer 1

`y'=1/(x^2+1)^(3/2)`

Solution :

`y=x/sqrt(x^2+1)`

Using Quotient Rule, which is

`y=f/g`, then `y'=(gf'-fg')/(g^2)`

similarly following for the given problem, yields

`y'=(sqrt(x^2+1)-x*1/(2sqrt(x^2+1))*(2x))/(sqrt(x^2+1))^2`

`y'=(sqrt(x^2+1)-x^2/(sqrt(x^2+1)))/(x^2+1)`

`y'=((x^2+1)-x^2)/(x^2+1)^(3/2)`

`y'=1/(x^2+1)^(3/2)`