What is (\partial)/(\partial x)(arctan(x^2+y^2)) ?

The answer to (\partial)/(\partial x)(arctan(x^2+y^2)) is (2x)/((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 >

(\partial)/(\partial x)(arctan(x^2+y^2))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\int \frac{1}{x 3 x} d x

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

t y^{^{'}} = (1 - y^{2})^{\frac{1}{2}}

\int \frac{e ^{2 x}}{x ^{2}} d x

What is (\partial)/(\partial x)(arctan(x^2+y^2)) ?
The answer to (\partial)/(\partial x)(arctan(x^2+y^2)) is (2x)/((x^2+y^2)^2+1)