What is derivative of x=(y^3)/(3+y) ?

The answer to derivative of x=(y^3)/(3+y) is (dy)/(dx)=(9+6y+y^2)/(y^2(9+2y))

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derivative of x=(y^3)/(3+y)

derivative of

x = \frac{y ^{3}}{3 + y}

\frac{d y}{d x} = \frac{9 + 6 y + y ^{2}}{y ^{2} ( 9 + 2 y )}

Solution steps

x = \frac{y ^{3}}{3 + y}

Treat

y

y (x)

Differentiate both sides:

1 = \frac{9 y ^{2} \frac{d y}{d x} + 2 \frac{d y}{d x} y ^{3}}{( 3 + y ) ^{2}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{9 + 6 y + y ^{2}}{y ^{2} ( 9 + 2 y )}

\frac{d y}{d x} = \frac{9 + 6 y + y ^{2}}{y ^{2} ( 9 + 2 y )}

x^{2} + y^{2} = 2 x y

v = 2 - 4 t - 6 t^{3}

4 y = - 8 x + 2 x + 0

y^{2} = x

x^{2} + y^{2} = 6 x + 4 y

What is derivative of x=(y^3)/(3+y) ?
The answer to derivative of x=(y^3)/(3+y) is (dy)/(dx)=(9+6y+y^2)/(y^2(9+2y))