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Question
Find `bb(dy/dx)` in the following:
x2 + xy + y2 = 100
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Solution
x2 + xy + y2 = 100
Differentiating both sides with respect to x,
⇒ `d/dx (x^2) + {x d/dx (y) + 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`
⇒ `2x + y + x dy/dx + 2y dy/dx = 0`
⇒ `(x + 2y)dy/dx + (2x + y) = 0`
⇒ `(x + 2y)dy/dx = -(2x + y)`
∴ `dy/dx = (-(2x + y))/(x + 2y)`
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