What is implicit (dy)/(dx),x^{1/2}+y^{1/2}=9 ?

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

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implicit (dy)/(dx),x^{1/2}+y^{1/2}=9

implicit derivative

\frac{d y}{d x}, 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}}

\int \frac{arcsin ^{3} ( x )}{1 - x ^{2}} d x

\frac{d}{d x} ((8 x^{2} - 14 x) e^{x})

\int t^{2} + 1 d t

\frac{d}{d x} (x - 2 y)

f (x) = x^{2} - 2 x - 8, at x = - 2

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