en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arctan(x/2)

Solution

derivative of

arctan (\frac{x}{2})

Solution

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

Solution steps

\frac{d}{d x} (arctan (\frac{x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Simplify

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

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

Popular Examples

limit as x approaches infinity of (ln(x))^{1/(x^2)}

x \to \infty lim ((ln (x))^{\frac{1}{x ^{2}}})

integral of x^4in(x)

\int x^{4} in (x) d x

y^{^{'}} + a^{2} y = 0

(\partial)/(\partial x)(-2sin(2x)-2xe^{5y})

\frac{\partial}{\partial x} (- 2 sin (2 x) - 2 x e^{5 y})

f(s)= s/(s^2+1)

f (s) = \frac{s}{s ^{2} + 1}

Frequently Asked Questions (FAQ)

What is the derivative of arctan(x/2) ?
The derivative of arctan(x/2) is 2/(x^2+4)
What is the first derivative of arctan(x/2) ?
The first derivative of arctan(x/2) is 2/(x^2+4)