What is implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10 ?

The answer to implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10 is (dy)/(dx)=-(y/x)^{1/3}

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implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10

implicit derivative

\frac{d y}{d x}, x^{(\frac{2}{3})} + y^{(\frac{2}{3})} = 10

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

Solution steps

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 10

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}}

What is implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10 ?
The answer to implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10 is (dy)/(dx)=-(y/x)^{1/3}