Question 5: Find dy/dx : x²+ xy + y² = 100
Class 12 - Math - Continuity and Differentiability
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given x^2+xy+y^2=100
by using implicit differentiation
differentiating both sides with respect to x
=>2x+(x*(dy/dx)+ y)+2y(dy/dx)=0
2x+xdy/dx+y+2ydy/dx=0
xdy/dx+2ydy/dx=-(y+2x)
dy/dx(x+2y)=-(y+2x)
dy/dx=-(y+2x)/(x+2y)
by using implicit differentiation
differentiating both sides with respect to x
=>2x+(x*(dy/dx)+ y)+2y(dy/dx)=0
2x+xdy/dx+y+2ydy/dx=0
xdy/dx+2ydy/dx=-(y+2x)
dy/dx(x+2y)=-(y+2x)
dy/dx=-(y+2x)/(x+2y)
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