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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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)

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)