How do you use implicit differentiation to find dy/dx given #y^2+xlny=3#?

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Answer 1 · 2016-09-11T15:42:06

#dy/dx = -(ylny)/(2y^2 + x)#

#d/dx(y^2 + xlny) = d/dx(3)#

#d/dx(y^2) + d/dx(xlny) = d/dx(3)#

#2y(dy/dx) + 1lny + x(1/y)(dy/dx) = 0#

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

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

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

#dy/dx = -(ylny)/(2y^2 + x)#

Hopefully this helps!