What is the derivative of arctan(x^2+y^2) ?

The derivative of arctan(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2+1}

What is the first derivative of arctan(x^2+y^2) ?

The first derivative of arctan(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2+1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d y} (y - 1)

\int (\frac{1}{cos ( x )}) d x

6 - 5 x^{2}

n = 1 \sum \infty \frac{5}{n ^{2} + 9}

\int_{\frac{1}{5}}^{3} 6 x ln (5 x) d x

What is the derivative of arctan(x^2+y^2) ?
The derivative of arctan(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2+1}
What is the first derivative of arctan(x^2+y^2) ?
The first derivative of arctan(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2+1}