X4-7x2y2-9y4-24xy2thendy-dx-

We have, x^4 + 7x^2y^2 + 9y^4 = 24xy^2 Differentiating w.r.t. x on both sides, 4x^3 + 7y^2(2x) + 7x^2.2ydydx + 36y^3dydx = 24[2yxdydx + y^2] 4x^3 + ...

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Byju's Answer

Standard VIII

Mathematics

Letters for Digits

x4+7x2y2+9y4=...

Question

$x^{4} + 7 x^{2} y^{2} + 9 y^{4} = 24 x y^{2} t h e n \frac{d y}{d x} =$

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Solution

We have,
$x^{4} + 7 x^{2} y^{2} + 9 y^{4} = 24 x y^{2}$
Differentiating w.r.t. x on both sides,
$4 x^{3} + 7 y^{2} (2 x) + 7 x^{2} .2 y \frac{d y}{d x} + 36 y^{3} \frac{d y}{d x} = 24 [2 y x \frac{d y}{d x} + y^{2}]$
$4 x^{3} + 14 x y^{2} + 14 x^{2} y \frac{d y}{d x} + 36 y^{3} \frac{d y}{d x} = 48 x y \frac{d y}{d x} + 24 y^{2}$
$\frac{d y}{d x} [14 x^{2} y + 36 y^{3} - 48 x y] = 24 y^{2} - 14 x y^{2} - 4 x^{3}$
$\frac{d y}{d x} = \frac{24 y^{2} - 14 x y^{2} - 4 x^{3}}{14 x^{2} y + 36 y^{3} - 48 x y}$

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x4+7x2y2+9y4=24xy2thendydx=

We have,x4+7x2y2+9y4=24xy2Differentiating w.r.t. x on both sides,4x3+7y2(2x)+7x2.2ydydx+36y3dydx=24[2yxdydx+y2]4x3+14xy2+14x2ydydx+36y3dydx=48xydydx+24y2dydx[14x2y+36y3−48xy]=24y2−14xy2−4x3dydx=24y2−14xy2−4x314x2y+36y3−48xy

$x^{4} + 7 x^{2} y^{2} + 9 y^{4} = 24 x y^{2} t h e n \frac{d y}{d x} =$