d/(dθ)(cot(ln(θ-cos(sqrt(θ)))))

Lösung

\frac{d}{d θ} (cot (ln (θ - cos (θ))))

- \frac{csc ^{2} ( ln ( θ - cos ( θ ) ) ) ( 2 θ + sin ( θ ) )}{2 θ ( θ - cos ( θ ) )}

Schritte zur Lösung

\frac{d}{d θ} (cot (ln (θ - cos (θ))))

Wende die Kettenregel an:

- csc^{2} (ln (θ - cos (θ))) \frac{d}{d θ} (ln (θ - cos (θ)))

= - csc^{2} (ln (θ - cos (θ))) \frac{d}{d θ} (ln (θ - cos (θ)))

\frac{d}{d θ} (ln (θ - cos (θ))) = \frac{2 θ + sin ( θ )}{2 θ ( θ - cos ( θ ) )}

= - csc^{2} (ln (θ - cos (θ))) \frac{2 θ + sin ( θ )}{2 θ ( θ - cos ( θ ) )}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{csc ^{2} ( ln ( θ - cos ( θ ) ) ) ( 2 θ + sin ( θ ) )}{2 θ ( θ - cos ( θ ) )}