(\partial)/(\partial k)(ln(sin(x/k)))

Lösung

\frac{\partial}{\partial k} (ln (sin (\frac{x}{k})))

- \frac{x cot ( \frac{x}{k} )}{k ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial k} (ln (sin (\frac{x}{k})))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{sin ( \frac{x}{k} )} \frac{\partial}{\partial k} (sin (\frac{x}{k}))

= \frac{1}{sin ( \frac{x}{k} )} \frac{\partial}{\partial k} (sin (\frac{x}{k}))

\frac{\partial}{\partial k} (sin (\frac{x}{k})) = - \frac{x cos ( \frac{x}{k} )}{k ^{2}}

= \frac{1}{sin ( \frac{x}{k} )} (- \frac{x cos ( \frac{x}{k} )}{k ^{2}})

Vereinfache

\frac{1}{sin ( \frac{x}{k} )} (- \frac{x cos ( \frac{x}{k} )}{k ^{2}}) : - \frac{x cot ( \frac{x}{k} )}{k ^{2}}

= - \frac{x cot ( \frac{x}{k} )}{k ^{2}}

\int \frac{x ^{2}}{4 x ^{3} + 7} d x

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{1}{x}))

(x^{2} - x) y^{^{'}} = y - 2 x y

d er i v a t i v e cos^{4} (θ + 5)

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