Question

Find dy/dx by implicit differentiation. √(x+y)=4+x^(2)y^(2). dy/dx=?

Answer 1

\[\frac{ d }{ dx }(\sqrt{x+y})=\frac{ d }{ dx }(4+x^{2}y^{2})\]
\[\frac{ 1 }{ 2\sqrt{x+y} }(1+y^{'})=0+2xy^{2}+2yx^{2}y^{'}\]
\[y^{'}=\frac{ 1-4xy^{2}\sqrt{x+y} }{ 4yx^{2}\sqrt{x+y}-1 }\]

Answer 2

thank you very much zekarias