What is derivative of x^3+y^3=9 ?

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

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derivative of x^3+y^3=9

derivative of

x^{3} + y^{3} = 9

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

Solution steps

x^{3} + y^{3} = 9

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

x^{2} + y^{2} - 3 x y = 1

7 x^{4} - 4 y = 4

4 x + 5 y = lo g_{10} (4 x - 3 y)

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

x^{y} = y^{2}

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