What is implicit x^{2/3}+y^{2/3}=4 ?

The answer to implicit x^{2/3}+y^{2/3}=4 is (dy)/(dx)=-(y/x)^{1/3}

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implicit x^{2/3}+y^{2/3}=4

implicit derivative

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4

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

Solution steps

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4

Treat

y

y (x)

Differentiate both sides:

\frac{2}{3 x ^{\frac{1}{3}}} + \frac{2 \frac{d y}{d x}}{3 y ^{\frac{1}{3}}} = 0

Isolate

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

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

\int (x^{2} + x) d x

\frac{\partial}{\partial t} (t)

\frac{\partial}{\partial x} (ln (y - x))

\frac{d}{d x} (\frac{x ^{6}}{2 - x ^{5}})

\frac{d}{d x} ((2.5)^{x})

What is implicit x^{2/3}+y^{2/3}=4 ?
The answer to implicit x^{2/3}+y^{2/3}=4 is (dy)/(dx)=-(y/x)^{1/3}