What is (\partial)/(\partial x)(ln(tan(x/2))) ?

The answer to (\partial)/(\partial x)(ln(tan(x/2))) is csc(x)

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(\partial)/(\partial x)(ln(tan(x/2)))

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

csc (x)

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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)

\int \frac{1 - x ^{2}}{x} d x

x \to 0 + lim (cos (x))

y^{^{''}} + 0.2 x^{2} - 0.35 x = 0

n = 1 \sum \infty \frac{1}{2 ^{3 n}}

f (x) = \frac{1}{2 x + 3}, at x = 2

What is (\partial)/(\partial x)(ln(tan(x/2))) ?
The answer to (\partial)/(\partial x)(ln(tan(x/2))) is csc(x)