What is (\partial)/(\partial x)(4arctan(xy)) ?

The answer to (\partial)/(\partial x)(4arctan(xy)) is (4y)/(x^2y^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(4arctan(xy))

\frac{\partial}{\partial x} (4 arctan (x y))

\frac{4 y}{x ^{2} y ^{2} + 1}

Solution steps

\frac{\partial}{\partial x} (4 arctan (x y))

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (arctan (x y))

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x y) = y

= 4 \cdot \frac{1}{( x y ) ^{2} + 1} y

Simplify

4 \cdot \frac{1}{( x y ) ^{2} + 1} y : \frac{4 y}{x ^{2} y ^{2} + 1}

= \frac{4 y}{x ^{2} y ^{2} + 1}

\int 12 d x

x \to 0 lim (\frac{x}{tan ( 2 x )})

d er i v a t i v e x 16 - x^{2}

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

\int 24 sin (x) d x

What is (\partial)/(\partial x)(4arctan(xy)) ?
The answer to (\partial)/(\partial x)(4arctan(xy)) is (4y)/(x^2y^2+1)