What is (\partial)/(\partial z)(8yarctan(x/z)) ?

The answer to (\partial)/(\partial z)(8yarctan(x/z)) is -(8yx)/(x^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 z)(8yarctan(x/z))

\frac{\partial}{\partial z} (8 y arctan (\frac{x}{z}))

- \frac{8 y x}{x ^{2} + z ^{2}}

Solution steps

\frac{\partial}{\partial z} (8 y arctan (\frac{x}{z}))

Treat

y, x

as constants

Take the constant out:

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

= 8 y \frac{\partial}{\partial z} (arctan (\frac{x}{z}))

Apply the chain rule:

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

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

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

= 8 y \frac{1}{( \frac{x}{z} ) ^{2} + 1} (- \frac{x}{z ^{2}})

Simplify

8 y \frac{1}{( \frac{x}{z} ) ^{2} + 1} (- \frac{x}{z ^{2}}) : - \frac{8 y x}{x ^{2} + z ^{2}}

= - \frac{8 y x}{x ^{2} + z ^{2}}

x \to 8 lim (5 x - 2)

\frac{d}{d x} (A x e^{\frac{x}{2}} + B)

\frac{d}{d x} (3 sin^{2} (x) cos (x))

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

\frac{d}{d x} (x \cdot x - 3 x)

What is (\partial)/(\partial z)(8yarctan(x/z)) ?
The answer to (\partial)/(\partial z)(8yarctan(x/z)) is -(8yx)/(x^2+z^2)