Question

Challenge to the best users:

Find the derivative of:

X ^2 = X + 3y / X - 3 y
Solve this for 90 points.

Answer 1

hey Mate here's your answer
x^2=x+3y/x-3y
x2×x-3y=x+3y
x3-3x^2y= x+3y
x^3= x+3y+3x^2y
x^3-x-3y=3x^2y
x^2-3y= 3x^2y
ok hope it helps
please click as brainliest

Answer 2

$Hey \:there!\\ \\ Solution:\\ \\ x^{2} = \frac{x + 3y}{x - 3y}\\ \\ Crossing\: Multiplying:\\ \\ x^{2} ( x - 3y ) = ( x + 3y )\\ \\ x^{3} - 3x^{2}y = x + 3y\\ \\ x^{3} - 3x^{2}y - x - 3y = 0\\ \\ Now,\: Differentiate\: Both\: Sides \:wrt \:x:\\ \\ 3x^{2} - ( 3x^{2} \frac{dy}{dx} + y\frac{d}{dx}×3x^{2}) - 1 - 3 \frac{dy}{dx} = 0\\ \\ 3x^{2} - 3x^{2}\frac{dy}{dx} - y( 6x ) - 1 - 3 \frac{dy}{dx} = 0\\ \\ Taking\: \frac{dy}{dx}\: Common:\\ \\ \frac{dy}{dx} ( -3x^{2} - 3 ) - 6xy + 3x^{2} - 1 = 0\\ \\ \frac{dy}{dx} ( - 3x^{2} - 3 ) = 6xy + 3x^{2} - 1 = 0\\ \\ -3 ( x^{2} + 1 ) \frac{dy}{dx} = 6xy - 3x^{2} + 1 \\ \\ 3 ( x^{2} + 1 ) \frac{dy}{dx} = 3x^{2} - 6xy - 1 \\ \\ \frac{dy}{dx} = \frac{3x^{2} - 6xy - 1}{3 ( x^{2} + 1 )}$



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