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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

y^{^{''}} - a y = 0

\frac{d}{d x} (e^{x} + c)

d er i v a t i v e f (x) = x^{2} + x + 1

\int \frac{1}{p - p ^{2}} d p

\frac{d}{d x} (arccsc (- x^{2}))

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