how do i find the derivative of a square root?
If your expression is \(u = { \sqrt{f(x)}}\)
then u = ( f(x) )1/2,
so u' = (1/2) ( f(x) )-1/2 f'(x).
As an example: if \(u = {\sqrt{sin(x)} }\)
then u' = (1/2) [sin(x)]-1/2 cos(x)
\(y=\sqrt{x}\\ y=x^{0.5}\\\\ \frac{dy}{dx}=0.5x^{-0.5}\\\\ \frac{dy}{dx}=\frac{1}{2\sqrt{x}}\\\\ \)
