Math

Find dx/dy by implicit differentiation
x^2y+y^2x

P.S: It's calculus

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  1. Differentiate with respect to y, recognizing that x is a function of y.

    You cannot "find" dx/dy unless you write an equation. You have only written a formula for a function g(x,y).

    If x^2*y + y^2*x = C (any constant), then
    x^2 + y*2x*dx/dy + 2yx + y^2 dx/dy = 0
    dx/dy(y^2x + y^2) = -x^2 -2yx
    dx/dy = -x(x-2y)/[y^2(1+x)]

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  2. I think you want this equal to a constant if you want a solutionyou want dx/dy so differentiate wrt y
    x^2 + y 2 x dx/dy+ y^2 dx/dy + x 2 y

    = x^2 + 2 xy dx/dy + y^2 dx/dy + 2 x y

    = dx/dy (2xy + y^2) + x^2 + 2xy

    now if the right hand were a constant, then that = 0 so
    dx/dy = -(x^2+2xy)/(y^2+2xy)

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  3. y = x^2y+y^2x

    dy/dx = 2y X^2y-1 + 2x Y^2x-1

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