What is (\partial)/(\partial x)(arccot(x/y)) ?

The answer to (\partial)/(\partial x)(arccot(x/y)) is -y/(x^2+y^2)

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(\partial)/(\partial x)(arccot(x/y))

\frac{\partial}{\partial x} (arccot (\frac{x}{y}))

- \frac{y}{x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (arccot (\frac{x}{y}))

Treat

y

as a constant

Apply the chain rule:

- \frac{1}{( \frac{x}{y} ) ^{2} + 1} \frac{\partial}{\partial x} (\frac{x}{y})

= - \frac{1}{( \frac{x}{y} ) ^{2} + 1} \frac{\partial}{\partial x} (\frac{x}{y})

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

= - \frac{1}{( \frac{x}{y} ) ^{2} + 1} \cdot \frac{1}{y}

Simplify

- \frac{1}{( \frac{x}{y} ) ^{2} + 1} \cdot \frac{1}{y} : - \frac{y}{x ^{2} + y ^{2}}

= - \frac{y}{x ^{2} + y ^{2}}

\frac{d}{d x} (\frac{x + 6}{x - 6})

\frac{d}{d x} (7 + 9 x)

x \to - 1.9 lim (2 sin (x))

x \to 1 - lim (\frac{4}{x - 1})

(x - 6) y^{^{'}} + y = x^{2} + 18

What is (\partial)/(\partial x)(arccot(x/y)) ?
The answer to (\partial)/(\partial x)(arccot(x/y)) is -y/(x^2+y^2)