What is the implicit derivative of #-2=ysqrt(x-y) #?

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Answer 1 · 2016-11-04T16:54:36

#:. dy/dx=-y/(2x-4y)#

#-2=ysqrt(x-y)#

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

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

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

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

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

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

#:. dy/dx=-y/(2x-4y)#