What is implicit (dy)/(dx),xy=9 ?

The answer to implicit (dy)/(dx),xy=9 is (dy)/(dx)=-y/x

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implicit (dy)/(dx),xy=9

implicit derivative

\frac{d y}{d x}, x y = 9

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

Solution steps

x y = 9

Treat

y

y (x)

Differentiate both sides:

y + x \frac{d y}{d x} = 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 (dy)/(dx),xy=9 ?
The answer to implicit (dy)/(dx),xy=9 is (dy)/(dx)=-y/x