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

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

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

implicit derivative

\frac{d y}{d x}, x y = cot (x y)

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

Solution steps

x y = cot (x y)

Treat

y

y (x)

Differentiate both sides:

y + x \frac{d y}{d x} = - csc^{2} (x y) (y + x \frac{d y}{d x})

Isolate

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

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

\frac{\partial}{\partial x} (\frac{z}{x} ln (y) + ln (x))

\int \frac{x}{2 + x} d x

f (x) = (- x^{3} - x^{2} + x) cos (x)

\frac{d y}{d x} = x + \frac{1}{5} y

\frac{d}{d x} (\frac{x ^{2} - 4}{x + 1})

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