d/(dθ)(5/(sin(θ)-2cos(θ)))

Lösung

\frac{d}{d θ} (\frac{5}{sin ( θ ) - 2 cos ( θ )})

- \frac{5 ( cos ( θ ) + 2 sin ( θ ) )}{( sin ( θ ) - 2 cos ( θ ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d θ} (\frac{5}{sin ( θ ) - 2 cos ( θ )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d θ} (\frac{1}{sin ( θ ) - 2 cos ( θ )})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 5 \frac{d}{d θ} ((sin (θ) - 2 cos (θ))^{- 1})

Wende die Kettenregel an:

- \frac{1}{( sin ( θ ) - 2 cos ( θ ) ) ^{2}} \frac{d}{d θ} (sin (θ) - 2 cos (θ))

= - \frac{1}{( sin ( θ ) - 2 cos ( θ ) ) ^{2}} \frac{d}{d θ} (sin (θ) - 2 cos (θ))

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

= 5 (- \frac{1}{( sin ( θ ) - 2 cos ( θ ) ) ^{2}} (cos (θ) + 2 sin (θ)))

Vereinfache

5 (- \frac{1}{( sin ( θ ) - 2 cos ( θ ) ) ^{2}} (cos (θ) + 2 sin (θ))) : - \frac{5 ( cos ( θ ) + 2 sin ( θ ) )}{( sin ( θ ) - 2 cos ( θ ) ) ^{2}}

= - \frac{5 ( cos ( θ ) + 2 sin ( θ ) )}{( sin ( θ ) - 2 cos ( θ ) ) ^{2}}

x^{2} \frac{d y}{d x} = x - x y

\int x^{2} - 6 x d x

d er i v a t i v e - \frac{1}{3} x^{2}

\frac{d}{d x} (ln (9 x^{2} - 11))

(t cos (t))^{^{'}}