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प्रश्न
if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`
उत्तर
We have `(x^2 + y^2) = xy`
Differentiating with respect to x, we get
`=> d/dx [(x^2 + y^2)^2] = d/dx (xy)`
`=> 2(x^2 + y^2) d/(dx) (x^2 + y^2) = x (dy)/(dx) + y d/dx (x)`
`=> 2(x^2 + y^2) (2x+ 2y dy/dx) = x (dy/dx) + y (1)`
`=> 4x (x^2 + y^2) + 4y (x^2 + y^2) dy/dx = x dy/dx + y`
`=> 4y(x^2 + y^2) dy/dx - x dy/dx = y - 4x (x^2 + y^2)`
`=> dy/dx [4y(x^2 + y^2) - x] = y - 4x(x^2 + y^2)`
`=> dy/dx = (y - 4x(x^2+y^2))/(4y(x^2 + y^2) - x)`
`=> dy/dx = (4x(x^2 + y^2)-y)/(x-4y(x^2 + y^2))`
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