What is (\partial)/(\partial y)(xarctan(y/z)) ?

The answer to (\partial)/(\partial y)(xarctan(y/z)) is (xz)/(y^2+z^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(xarctan(y/z))

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to + (- 3) lim (2 x + 5)

g (u) = 2 u + 3 u

x \to 0 lim (- 2 x + 1)

\frac{d}{d x} (\frac{a ^{x}}{ln ( a )})

\frac{d}{d x} (\frac{e ^{x}}{( 1 + e ^{2 x} ) ^{\frac{3}{2}}})

What is (\partial)/(\partial y)(xarctan(y/z)) ?
The answer to (\partial)/(\partial y)(xarctan(y/z)) is (xz)/(y^2+z^2)