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)

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

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

Simplify

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

= csc (x)

\frac{d}{d x} (\frac{9 - x ^{2}}{32 x})

s (t) = 14 t^{2} + 840 t

0

x \to 0 lim (\frac{0 \cdot x ^{6}}{x ^{9}})

3 y^{^{''}} + 75 y = 0

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)