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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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)

4 e^{2} x

\frac{( x ^{2} )}{10}

\frac{d}{d q} ((1 + sec (q)) sin (q))

\frac{d}{d t} (5 t^{4} + 4 t^{3} + 2 t^{2} + 5 + 4)

\frac{d}{d r} (\frac{g \cdot ( m _{1} \cdot m _{2} )}{( r ^{2} )})

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)