1. ## Implicit Differentiation #1

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

2. Originally Posted by skeske1234
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:

$(x+y)^2=x^2+y^2~\implies~2(x+y)(1+y')=2x+2y\cdot y'$

${\color{white}(x+y)^2=x^2+y^2}~\implies~ x+xy'+y+yy'=x+yy'$

${\color{white}(x+y)^2=x^2+y^2}~\implies~ xy'+y=0$

${\color{white}(x+y)^2=x^2+y^2}~\implies~y'=-\dfrac yx$