d/(dθ)(({x}(θ))(3(1-cos(θ))))

Lösung

\frac{d}{d θ} ((x (θ)) (3 (1 - cos (θ))))

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

Schritte zur Lösung

\frac{d}{d θ} ((x (θ)) (3 (1 - cos (θ))))

Entferne die Konstante:

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

= 3 \frac{d}{d θ} (x (θ) (1 - cos (θ)))

Wende die Produktregel an:

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

f = x (θ), g = 1 - cos (θ)

= 3 (\frac{d}{d θ} (x (θ)) (1 - cos (θ)) + \frac{d}{d θ} (1 - cos (θ)) x (θ))

\frac{d}{d θ} (1 - cos (θ)) = sin (θ)

= 3 (\frac{d}{d θ} (x (θ)) (1 - cos (θ)) + sin (θ) x (θ))

e x p an d - \frac{- 5 x + 4}{2 ln ( 5 ) x ( - x + 1 )}

s im pl i f y (x - 4) (x + 7) (x - 2) (x + 2)

s im pl i f y (1 - \frac{1}{x}) (1 + \frac{1}{z ^{2}}) (1 + \frac{1}{z})

e x p an d \frac{4 s + 2 s ^{2} + 8}{( s ^{2} + 4 ) ( s + 1 ) ^{2}}

e x p an d \frac{6 x ^{2} + 21 x + 11}{( x ^{2} + 3 ) ( x + 5 )}