Question

sqrtx+y=x using implicit differentiation

Answer 1

differentiate each term
\[\rightarrow \frac{1}{2 \sqrt{x}} + \frac{dy}{dx} = 1\]

Answer 2

or is it
\[\sqrt{x+y} = x\]
?

in which case you would use the chain rule
\[\frac{1 + \frac{dy}{dx}}{2 \sqrt{x+y}} = 1\]