d/(dθ)(({x}(θ))(θ-sin(θ)))

Lösung

\frac{d}{d θ} ((x (θ)) (θ - sin (θ)))

\frac{d}{d θ} (x (θ)) (θ - sin (θ)) + (1 - cos (θ)) x (θ)

Schritte zur Lösung

\frac{d}{d θ} ((x (θ)) (θ - sin (θ)))

Wende die Produktregel an:

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

f = x (θ), g = θ - sin (θ)

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

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

= \frac{d}{d θ} (x (θ)) (θ - sin (θ)) + (1 - cos (θ)) x (θ)

e x p an d (e^{x} sin (2 x)) (e^{x} cos (2 x) - 2 e^{x} sin (2 x))

e x p an d - 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

e x p an d \frac{x + 1}{2 ( x - 1 ) ( 4 x + 1 )}

e x p an d (x + 5) l e f t (x - 5)

e x p an d (r + sin (θ) - cos (θ)) d r