Question

Find dy/dx when :
(i) x²/9 + y²/4=1​

Answer 1

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$\frac{d \: \: ( \frac{ {x}^{2} }{9} + \frac{ {y}^{2} }{4} )}{dx} = \frac{d \: 1}{dx} = 0\\ \implies \: \frac{d \: \: \frac{ {x}^{2} }{9} }{dx} + \frac{d \: \: \frac{ {y}^{2} }{4} }{dx} = 0 \\ \implies \: \frac{1}{9} \times 2x + \frac{1}{ \cancel 4 \: 2} \times \cancel 2y \times \frac{dy}{dx} = 0 \\ \implies \: \frac{y}{2} \times \frac{dy}{dx} = - \frac{2x}{9} \\ \implies \: \frac{dy}{dx} = - \frac{4x}{9y} \\ \\ \therefore \: \frac{dy}{dx} = - \frac{4x}{9y}$