find dy/dx
(x+y)^2=x^2+y^2
i keep getting 1 as the answer but the answer in the back says -y/x
Use the chain rule:
$\displaystyle (x+y)^2=x^2+y^2~\implies~2(x+y)(1+y')=2x+2y\cdot y'$
$\displaystyle {\color{white}(x+y)^2=x^2+y^2}~\implies~ x+xy'+y+yy'=x+yy'$
$\displaystyle {\color{white}(x+y)^2=x^2+y^2}~\implies~ xy'+y=0$
$\displaystyle {\color{white}(x+y)^2=x^2+y^2}~\implies~y'=-\dfrac yx$