Question

How do you find the derivative of `f(x)=3sqrt(x)-(2/sqrt(x))`?

Answer 1

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

In Radicals,
`f'(x)=(3x+2)/(2xsqrtx).`

Explanation:

`f(x)=3sqrtx-2/sqrtx=3*x^(1/2)-2*x^(-1/2)`.
`f'(x)=3*{(x)^(1/2)}'-2*{x^(-1/2)}'=3*1/2*x^(1/2-1)-2(-1/2)*x^(-1/2-1)=3/2*x^(-1/2)+x^(-3/2)`

Using Radicals,
`f'(x)=3/(2sqrtx)+1/(xsqrtx)=(3x+2)/(2xsqrtx).`