How do you implicitly differentiate #7=3x-y+y^2x#?

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Answer 1 · 2015-12-17T22:44:55

#dy/dx=(y^2+3)/(1-2xy)#

The challenge in this problem lies in using the product rule for the #y^2x# term.

#d/dx[7=3x-y+y^2x]#

#0=3-dy/dx+d/dx[y^2]*x+d/dx[x]*y^2#

#0=3-dy/dx+2xy*dy/dx+y^2#

#dy/dx-2xy*dy/dx=y^2+3#

#dy/dx(1-2xy)=y^2+3#

#dy/dx=(y^2+3)/(1-2xy)#