en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(tan(x/2))

Solution

\frac{d}{d x} (ln (tan (\frac{x}{2})))

Solution

csc (x)

Solution steps

\frac{d}{d x} (ln (tan (\frac{x}{2})))

Apply the chain rule:

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

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

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

= \frac{1}{tan ( \frac{x}{2} )} sec^{2} (\frac{x}{2}) \frac{1}{2}

Simplify

\frac{1}{tan ( \frac{x}{2} )} sec^{2} (\frac{x}{2}) \frac{1}{2} : csc (x)

= csc (x)

Graph

Popular Examples

limit as x approaches-2 of (1-x^2)/(x+2)

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

inverse oflaplace (e^{-5s})/(s+1)inverse laplace

\frac{e ^{- 5 s}}{s + 1}

limit as x approaches-2+of (2x-1)/(x+2)

x \to - 2 + lim (\frac{2 x - 1}{x + 2})

y^{''}+4y=sin^2(x)

y^{^{''}} + 4 y = sin^{2} (x)

integral of \sqrt[3]{tan(4x)}sec^2(4x)

\int 3 tan (4 x) sec^{2} (4 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(tan(x/2)) ?
The derivative of ln(tan(x/2)) is csc(x)
What is the first derivative of ln(tan(x/2)) ?
The first derivative of ln(tan(x/2)) is csc(x)