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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{5 - 5 x}{1 - x} d x

x^{^{''}} + 8 x^{^{'}} + 16 x = 0

\frac{d}{d x} (5 x - 8)

X^{\frac{9}{6}}, 7

\frac{d}{d x} (tan (3^{x}))

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