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Question
Find `dx/dy` in the following.
x2 + xy + y2 = 100
Solution
Since, x2 + xy + y2 = 100
Differentiating both sides with respect to x,
`=> d/dx (x^2) + {x dy/dx + y d/dx (x)} + d/dx (y^2) = d/dx (100)`
`=> 2x = x dy/dx + y xx 1 + 2y dy/dx = 0`
`=> 2x + x dy/dx + y + 2y dy/dx = 0`
`=> x dy/dx + 2y dy/dx = -2 x - 1`
`=> dy/dx (x + 2y) = - (2x - y)`
`dy/dx = (- 2x + y)/(x + 2y)`
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