What is (\partial)/(\partial x)(z*arctan(y/x)) ?

The answer to (\partial)/(\partial x)(z*arctan(y/x)) is -(zy)/(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)(z*arctan(y/x))

\frac{\partial}{\partial x} (z \cdot arctan (\frac{y}{x}))

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

= z \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}}

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

Simplify

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

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

\int_{2}^{\infty} \frac{8 cos ( \frac{π}{x} )}{x ^{2}} d x

h \to + 0 lim (\frac{\frac{1}{a + h} - \frac{1}{a}}{h})

\frac{d}{d t} (t)

\int t^{- 3} d t

\int \frac{x ^{3}}{25 + x ^{2}} d x

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