What is derivative of x^3y^2-2y=4 ?

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

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derivative of x^3y^2-2y=4

derivative of

x^{3} y^{2} - 2 y = 4

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

Solution steps

x^{3} y^{2} - 2 y = 4

Treat

y

y (x)

Differentiate both sides:

3 x^{2} y^{2} + 2 y \frac{d y}{d x} x^{3} - 2 \frac{d y}{d x} = 0

Isolate

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

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

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

x^{2} - y^{2} = 2

x = tan^{2} (y)

y^{2} = 40 x

x y = c^{2}

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