en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dy)(arctan(x/y))

Solution

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

Solution

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of \sqrt[8]{x^9}

derivative of arctan(x^4)

\frac{d}{d x} (arctan (x^{4}))

f(t)=sqrt((t^2+1)/(t^2-1))

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

integral from 1 to infinity of 1/(5x+2)

\int_{1}^{\infty} \frac{1}{5 x + 2} d x

derivative of log_{7}(x^2)

\frac{d}{d x} (lo g_{7} (x^{2}))

Frequently Asked Questions (FAQ)

What is the d/(dy)(arctan(x/y)) ?
The d/(dy)(arctan(x/y)) is -x/(x^2+y^2)
What is the first d/(dy)(arctan(x/y)) ?
The first d/(dy)(arctan(x/y)) is -x/(x^2+y^2)