What is implicit sqrt(x)+sqrt(y)=8 ?

The answer to implicit sqrt(x)+sqrt(y)=8 is (dy)/(dx)=-sqrt(y/x)

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implicit sqrt(x)+sqrt(y)=8

implicit derivative

x + y = 8

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

Solution steps

x + y = 8

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

What is implicit sqrt(x)+sqrt(y)=8 ?
The answer to implicit sqrt(x)+sqrt(y)=8 is (dy)/(dx)=-sqrt(y/x)