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Question

By implicit differentiation w.r.t x, obtain the relation satisfied by dy/dx 

y² +5 yx - x² = 7

Answer 1

The Function is y² + 5yx - x² = 7

Differentiate it with respect to x.

2y y' + 5(y + xy') - 2x = 0

2y y' + 5y + 5 x y' - 2x = 0

y'(2y + 5x) +5y - 2x = 0

y' = -(5y - 2x) / (5x + 2y)

y' = (2x - 5y) / (5x + 2y)

Therefore the Derivative is y' = (2x - 5y) / (5x + 2y).