What is implicit x^{1/2}+y^{1/2}=9 ?

The answer to implicit x^{1/2}+y^{1/2}=9 is (dy)/(dx)=-(y/x)^{1/2}

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implicit x^{1/2}+y^{1/2}=9

implicit derivative

x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9

\frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{2}}

Solution steps

x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{2}}

\frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{2}}

\frac{d}{d x} (\frac{x + 9}{x - 9})

x \to 0 lim (\frac{( 1 + x ) ^{7} - 1}{x})

\frac{\partial}{\partial x} (ln (e^{x} + e^{y} + e^{z}))

\int x^{3} sin (4 x) d x

\frac{5 x ^{4} - 3 x ^{3}}{x ^{5}}

What is implicit x^{1/2}+y^{1/2}=9 ?
The answer to implicit x^{1/2}+y^{1/2}=9 is (dy)/(dx)=-(y/x)^{1/2}