Question

How do you differentiate `x / (x^2 + 1)^(1/2)`?

Answer 1

`d/dx ( x/(x^2+1)^(1/2)) =1/(x^2+1)^(3/2)`

Explanation:

Using the quotient rule:

`d/dx ( x/(x^2+1)^(1/2)) = ( (x^2+1)^(1/2) - x (2x)/(2(x^2+1)^(1/2)))/(x^2+1)`

`d/dx ( x/(x^2+1)^(1/2)) = (x^2 +1 -x^2)/(x^2+1)^(3/2)`

`d/dx ( x/(x^2+1)^(1/2)) =1/(x^2+1)^(3/2)`