What is (\partial)/(\partial x)(3arctan(y/x)) ?

The answer to (\partial)/(\partial x)(3arctan(y/x)) is -(3y)/(y^2+x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(3arctan(y/x))

\frac{\partial}{\partial x} (3 arctan (\frac{y}{x}))

- \frac{3 y}{y ^{2} + x ^{2}}

Solution steps

\frac{\partial}{\partial x} (3 arctan (\frac{y}{x}))

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (arctan (\frac{y}{x}))

Apply the chain rule:

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

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

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

= 3 \cdot \frac{1}{( \frac{y}{x} ) ^{2} + 1} (- \frac{y}{x ^{2}})

Simplify

3 \cdot \frac{1}{( \frac{y}{x} ) ^{2} + 1} (- \frac{y}{x ^{2}}) : - \frac{3 y}{y ^{2} + x ^{2}}

= - \frac{3 y}{y ^{2} + x ^{2}}

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 5} d x

\frac{d}{d y} (\frac{x}{y})

x^{2} - 7 x - 24, - x^{2} + 3 x + 4

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

What is (\partial)/(\partial x)(3arctan(y/x)) ?
The answer to (\partial)/(\partial x)(3arctan(y/x)) is -(3y)/(y^2+x^2)