en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(arctan(t/2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of sqrt(x^2+5)derivative of

x^{2} + 5

derivative of y=(sec(x))/(1+sec(x))derivative of

y = \frac{sec ( x )}{1 + sec ( x )}

integral of 19sin^{-3/2}(x)cos^3(x)

\int 19 sin^{- \frac{3}{2}} (x) cos^{3} (x) d x

derivative of f(x)=(4-x^2)/(8+x^2)derivative of

f (x) = \frac{4 - x ^{2}}{8 + x ^{2}}

integral of 2x(6x^2-12)^2

\int 2 x (6 x^{2} - 12)^{2} d x

Frequently Asked Questions (FAQ)

What is the d/(dt)(arctan(t/2)) ?
The d/(dt)(arctan(t/2)) is 2/(t^2+4)
What is the first d/(dt)(arctan(t/2)) ?
The first d/(dt)(arctan(t/2)) is 2/(t^2+4)