What is implicit (dy)/(dx),xy=1 ?

The answer to implicit (dy)/(dx),xy=1 is (dy)/(dx)=-y/x

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implicit (dy)/(dx),xy=1

implicit derivative

\frac{d y}{d x}, x y = 1

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

Solution steps

x y = 1

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}

f (x) = x + \frac{1}{x}

x \to a + lim (\frac{cos ( x ) ln ( x - a )}{ln ( e ^{x} - e ^{a} )})

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

∣ x ∣, \frac{x}{2} + 3

x^{3} - 4 x^{2} - 9 x + 9

What is implicit (dy)/(dx),xy=1 ?
The answer to implicit (dy)/(dx),xy=1 is (dy)/(dx)=-y/x