d/(dθ)((x(θ))(r(θ)*θ-r(θ)sin(θ)))

Lösung

\frac{d}{d θ} ((x (θ)) (r (θ) \cdot θ - r (θ) sin (θ)))

\frac{d}{d θ} (x (θ)) (r (θ) θ - r (θ) sin (θ)) + (θ \frac{d}{d θ} (r (θ)) + r (θ) - sin (θ) \frac{d}{d θ} (r (θ)) - cos (θ) r (θ)) x (θ)

Schritte zur Lösung

\frac{d}{d θ} ((x (θ)) (r (θ) θ - r (θ) sin (θ)))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x (θ), g = r (θ) θ - r (θ) sin (θ)

= \frac{d}{d θ} (x (θ)) (r (θ) θ - r (θ) sin (θ)) + \frac{d}{d θ} (r (θ) θ - r (θ) sin (θ)) x (θ)

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

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

e x p an d \frac{- e ^{- s} s - e ^{- s} + 1}{s ^{2} ( 1 - e ^{- s} )}

e x p an d \frac{x ^{2}}{2 ( x - 7 ) ^{2}}

e x p an d (0 - 0.5) (0 - 1) (0 - 1.5) (0 - 2)

e x p an d lo g_{3} (9) + 3

e x p an d \frac{3 x + 11}{( x + 3 ) ( 3 x + 1 )}