What is derivative of x^2(x-2y)=x+2y ?

The answer to derivative of x^2(x-2y)=x+2y is (dy)/(dx)=-(1-3x^2+4xy)/(2(x^2+1))

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derivative of x^2(x-2y)=x+2y

derivative of

x^{2} (x - 2 y) = x + 2 y

\frac{d y}{d x} = - \frac{1 - 3 x ^{2} + 4 x y}{2 ( x ^{2} + 1 )}

Solution steps

x^{2} (x - 2 y) = x + 2 y

Treat

y

y (x)

Differentiate both sides:

3 x^{2} - 2 x^{2} \frac{d y}{d x} - 4 x y = 1 + 2 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{1 - 3 x ^{2} + 4 x y}{2 ( x ^{2} + 1 )}

\frac{d y}{d x} = - \frac{1 - 3 x ^{2} + 4 x y}{2 ( x ^{2} + 1 )}

p = i^{2} r

x (x + i) + y (y - i) + i = 13

x^{2} = 2 + t

y^{2} = 4 a (x + a)

x = \frac{( 1 + t ) ^{3}}{t ^{2}}

What is derivative of x^2(x-2y)=x+2y ?
The answer to derivative of x^2(x-2y)=x+2y is (dy)/(dx)=-(1-3x^2+4xy)/(2(x^2+1))