What is implicit (dx)/(dy),xy=2 ?

The answer to implicit (dx)/(dy),xy=2 is (dx)/(dy)=-x/y

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implicit (dx)/(dy),xy=2

implicit derivative

\frac{d x}{d y}, x y = 2

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

Solution steps

x y = 2

Treat

x

x (y)

Differentiate both sides:

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

Isolate

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

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

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\int_{1}^{e^{5}} x^{5} ln (x) d x

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What is implicit (dx)/(dy),xy=2 ?
The answer to implicit (dx)/(dy),xy=2 is (dx)/(dy)=-x/y