What is (\partial)/(\partial x)(1/(2pi)arctan(x/y)) ?

The answer to (\partial)/(\partial x)(1/(2pi)arctan(x/y)) is y/(2pi(x^2+y^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(1/(2pi)arctan(x/y))

\frac{\partial}{\partial x} (\frac{1}{2 π} arctan (\frac{x}{y}))

\frac{y}{2 π ( x ^{2} + y ^{2} )}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2 π} arctan (\frac{x}{y}))

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{2 π} \frac{\partial}{\partial x} (arctan (\frac{x}{y}))

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

Simplify

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

= \frac{y}{2 π ( x ^{2} + y ^{2} )}

y^{^{'}} = \frac{x y}{x ^{2} - 1}

(- 7, - 9), (1, 3)

\int_{1}^{e^{2}} \frac{ln ^{4} ( x ^{2} )}{x} d x

ln (1 - 5 y)

\frac{1}{s ^{2} + 9 s + 9}

What is (\partial)/(\partial x)(1/(2pi)arctan(x/y)) ?
The answer to (\partial)/(\partial x)(1/(2pi)arctan(x/y)) is y/(2pi(x^2+y^2))