What is (\partial)/(\partial x)(arctan(t/x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(arctan(t/x))

\frac{\partial}{\partial x} (arctan (\frac{t}{x}))

- \frac{t}{t ^{2} + x ^{2}}

Solution steps

\frac{\partial}{\partial x} (arctan (\frac{t}{x}))

Treat

t

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( \frac{t}{x} ) ^{2} + 1} (- \frac{t}{x ^{2}}) : - \frac{t}{t ^{2} + x ^{2}}

= - \frac{t}{t ^{2} + x ^{2}}

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