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

Lösung

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

csc (x)

Schritte zur Lösung

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

Wende die Kettenregel an:

\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}

Vereinfache

\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}}

\frac{d}{d x} (y cos (x))