DIfferentiate: $3 x^{2} - 8 x y + 5 y^{2} = 0$ .

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Solution

$3 x^{2} - 8 x y + 5 y^{2} = 0$ .
Differentiating w.r.t $x$
$6 x - 8 (x \frac{d y}{d x} + y) + 10 y \frac{d y}{d x} = 0$
$\Rightarrow 6 x - 8 x \frac{d y}{d x} - 8 y + 10 y \frac{d y}{d x} = 0$
$\Rightarrow (- 8 x + 10 y) \frac{d y}{d x} = 8 y - 6 x$
$\Rightarrow 2 (5 y - 4 x) \frac{d y}{d x} = 2 (4 y - 3 x)$
$∴ \frac{d y}{d x} = \frac{3 x - 4 y}{4 x - 5 y}$

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DIfferentiate: 3x2−8xy+5y2=0.

3x2−8xy+5y2=0.Differentiating w.r.t x6x−8(xdydx+y)+10ydydx=0⇒6x−8xdydx−8y+10ydydx=0⇒(−8x+10y)dydx=8y−6x⇒2(5y−4x)dydx=2(4y−3x)∴dydx=3x−4y4x−5y

DIfferentiate: $3 x^{2} - 8 x y + 5 y^{2} = 0$ .