Derivative question in calculus 1?

Question

what is the derivative of y=(8+x)/sqrt(x)

Answer 1

The function y = (8 + x)/(√x)

Apply the derivative on each side with respect of x.

Apply the quotient rule in derivatives d/dx (u/v) = [vu' - uv']/v²

u = 8 + x , v = √x

u' = 1, v' = 1/(2√x)

y' = {(√x)(1) - (8 + x)[1/(2√x)]}/(√x)²

y' = {√x - [(8 + x)/2√x]}/x

y' = {[2x - 8 - x ]/2√x}/x

y' = (x - 8)/(2x√x)