Question

How do you find the derivative of `f(x)= (x+1)/sqrtx`?

Answer 1

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

OR, `f'(x)=1/2{1/sqrtx-1/(x*sqrtx)}=1/2{(x-1)/(xsqrtx)}=(x-1)/(2xsqrtx).`

Explanation:

`f(x)=(x+1)/sqrtx=x/sqrtx+1/sqrtx=sqrtx+1/sqrtx=x^(1/2)+x^(-1/2).`

Therefore, `f'(x)=1/2*x^(1/2-1)+(-1/2)*x^(-1/2-1)`
`:. f'(x)=1/2(x^(-1/2)-x^(-3/2)),`

OR, `f'(x)=1/2{1/sqrtx-1/(x*sqrtx)}=1/2{(x-1)/(xsqrtx)}=(x-1)/(2xsqrtx).`