second derivative x^2 +3y^2 =5


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Question Number 117557 by abdullahquwatan last updated on 12/Oct/20

$second derivative$ $x^{2} + 3 y^{2} = 5$
	Answered by Dwaipayan Shikari last updated on 12/Oct/20

	$2 x + 6 y \frac{d y}{d x} = 0 \Rightarrow \frac{d y}{d x} = - \frac{x}{3 y}$ $2 + 6 y \frac{d^{2} y}{{d x}^{2}} + 6 {(\frac{d y}{d x})}^{2} = 0$ $2 + 6 y \frac{d^{2} y}{{d x}^{2}} + \frac{6 x^{2}}{9 y^{2}} = 0$ $6 y \frac{d^{2} y}{{d x}^{2}} = - \frac{6 x^{2} + 18 y^{2}}{9 y^{2}}$ $\frac{d^{2} y}{{d x}^{2}} = - \frac{6 x^{2} + 18 y^{2}}{54 y^{3}} = - \frac{x^{2} + 3 y^{2}}{9 y^{3}}$
	Commented by abdullahquwatan last updated on 12/Oct/20

	$thank you sir$
	Commented by abdullahquwatan last updated on 12/Oct/20

	$sir 2 + 6 y \frac{d^{2} y}{{d x}^{2}} + \frac{6 x^{2}}{9 y^{2}} ?$
	Commented by abdullahquwatan last updated on 12/Oct/20

	$sir 2 + 6 y \frac{d^{2} y}{{d x}^{2}} + \frac{6 x^{2}}{9 y^{2}} ?$
	Commented by Dwaipayan Shikari last updated on 12/Oct/20

	$O h y e s! t h a t w a s a m i s t a k e$
	Commented by abdullahquwatan last updated on 12/Oct/20

	$thank you sir$
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