`f(x) = 3x/(sqrt(x^2 + 1))` Find the derivative of the function.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`f(x)=3x/sqrt(x^2+1)`

Using the quotient rule of the derivative,

`f'(x)=3((sqrt(x^2+1)-xd/(dx)(sqrt(x^2+1)))/((sqrt(x^2+1))^2))`

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

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

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

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

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