Question

sqrt(x+y)= 4+ x^2y^2
I am having a lot of trouble working this out. Please show work

Answer 1

What did u want really?

Answer 2

I dont know where i'm messing this one up. I've tried taking the derivative of each piece and i think i'm screwing that up somehow

Answer 3

You want to derivate it?

Answer 4

its an implicit differentiation, so i know u need to derive each piece to start

Answer 5

i need to solve for y'

Answer 6

\[\frac{ d }{ dx }((x+y)^{\frac{ 1 }{ 2 }})=\frac{ d }{ dx }(4+x^{2}+y^{2})\]
\[\frac{ 1 }{ 2 }(x+y)^{\frac{- 1 }{ 2 }}(1+y^{'})=2x+2yy^{'}\]
\[\frac{ 1 }{ 2 }(x+y)^{\frac{- 1 }{ 2 }}+y^{'}\frac{ 1 }{ 2 }(x+y)^{\frac{- 1 }{ 2 }}=2x+2yy^{'}\]
\[\frac{ 1 }{ 2 }(x+y)^{\frac{- 1 }{ 2 }}-2x =2yy^{'} -\frac{ 1 }{ 2 }(x+y)^{\frac{- 1 }{ 2 }}\]
\[\frac{ 1 }{ 2 }(x+y)^{\frac{- 1 }{ 2 }}-2x =2yy^{'} -\frac{ 1 }{ 2 }(x+y)^{\frac{- 1 }{ 2 }}\]\[y^{'}=\frac{ 1-4x \sqrt{x+y} }{ y \sqrt{x+y}-1 }\]