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

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

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implicit 3x^3+2y^3=12

implicit derivative

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

9 x^{2} + 6 y^{2} \frac{d y}{d x} = 0

Isolate

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

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

\frac{d y}{d x} = \frac{x + 6}{x + 1}

\int \frac{1 + x ^{6}}{x ^{2}} d x

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y^{^{''}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = 0

\int 7 e^{7 x} d x

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