- #1

karush

Gold Member

MHB

- 3,269

- 5

Find y' $\sqrt{x}+\sqrt{y}=1$

\begin{array}{lll}

\textit{isolate }y

&\sqrt{y}=1-\sqrt{x}

&(1)\\ \\

\textit{square both sides}

&y=(1-\sqrt{x})^2

&(2)\\ \\

\textit{differentiate both sides}

&y'=2\left(1-\sqrt{x}\right)\left(-\dfrac{1}{2\sqrt{x}}\right)&

(3)\\ \\

\textit{simplify}

&y'=-\dfrac{1-\sqrt{x}}{\sqrt{x}}

&(4)

\end{array}

well we could rationalize the denominator but why?

hopefully correct