How do you use implicit differentiation to find dy/dx given #x^2+y^2=2#?

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Answer 1 · 2017-10-24T07:37:29

#(dy)/(dx)=-x/y#

we want

#d/(dx)(x^2+y^2=2)#

we differentiate each term #wrt" " x#and when we differentiate #y# we just multiply that term by #(dy)/(dx)# by virtue of the chain rule

#d/(dx)(x^2+y^2=2)#

#=>d/(dx)(x^2)+d/(dx)(y^2)=d/(dx)(2)#

#2x+2y(dy)/(dx)=0#

now rearrange for #(dy)/(dx)#

2y(dy)/(dx)=-2x#

#=>(dy)/(dx)=-x/y#