What is implicit x^2+y^3=12 ?

The answer to implicit x^2+y^3=12 is (dy)/(dx)=-(2x)/(3y^2)

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implicit x^2+y^3=12

implicit derivative

x^{2} + y^{3} = 12

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

Solution steps

x^{2} + y^{3} = 12

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\frac{d}{d x} (9 e^{x} + 5)

\frac{16}{( s + 4 ) ^{2}}

\frac{d y}{d x} - 5 y = 0

\int \frac{1}{sin ^{2} ( u )} d u

\frac{d}{d x} ((1 + x)^{k})

What is implicit x^2+y^3=12 ?
The answer to implicit x^2+y^3=12 is (dy)/(dx)=-(2x)/(3y^2)