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

The answer to (\partial)/(\partial x)(arcot(y/x)) is (arycsc^2(y/x))/(x^2)

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(\partial)/(\partial x)(arcot(y/x))

\frac{\partial}{\partial x} (a r cot (\frac{y}{x}))

\frac{a ry csc ^{2} ( \frac{y}{x} )}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (a r cot (\frac{y}{x}))

Treat

a, r, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a r \frac{\partial}{\partial x} (cot (\frac{y}{x}))

Apply the chain rule:

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

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

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

= a r (- csc^{2} (\frac{y}{x}) (- \frac{y}{x ^{2}}))

Simplify

a r (- csc^{2} (\frac{y}{x}) (- \frac{y}{x ^{2}})) : \frac{a ry csc ^{2} ( \frac{y}{x} )}{x ^{2}}

= \frac{a ry csc ^{2} ( \frac{y}{x} )}{x ^{2}}

y = e^{2 e^{x}}

x \to 3 lim (x^{2} - x - 6)

\int_{1}^{8} 7 \frac{ln ( x )}{x ^{2}} d x

\frac{s - 2}{s ^{2} - 7 s + 6}

What is (\partial)/(\partial x)(arcot(y/x)) ?
The answer to (\partial)/(\partial x)(arcot(y/x)) is (arycsc^2(y/x))/(x^2)