## Thomas' Calculus 13th Edition

$y'=2(\frac{2x^{1/2}}{2x^{1/2}+1})\times\frac{x^{-1/2}}{(2x^{1/2}+1)^2}$
Take the derivative of the equation using Power Rule, Chain Rule, and Quotient Rule: $y'=2(\frac{2x^{1/2}}{2x^{1/2}+1})\times\frac{(2x^{1/2}+1)(2\times\frac{1}{2}x^{-1/2})-(2x^{1/2})(2\times\frac{1}{2}x^{-1/2}+0)}{(2x^{1/2}+1)^2}$ $=2(\frac{2x^{1/2}}{2x^{1/2}+1})\times\frac{2+x^{-1/2}-2}{(2x^{1/2}+1)^2}=2(\frac{2x^{1/2}}{2x^{1/2}+1})\times\frac{x^{-1/2}}{(2x^{1/2}+1)^2}$