d/(dθ)((x)(c+v(x,θ)cos(θ)))

Lösung

\frac{d}{d θ} ((x) (c + v (x, θ) cos (θ)))

x (0 + (\frac{d}{d θ} (v (x, θ)) cos (θ) + (- sin (θ)) v (x, θ)))

Schritte zur Lösung

\frac{d}{d θ} ((x) (c + v (x, θ) cos (θ)))

Behandle

c, x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d θ} (c + v (x, θ) cos (θ))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{d c}{d θ} + \frac{d}{d θ} (v (x, θ) cos (θ)))

\frac{d c}{d θ} = 0

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

= x (0 + (\frac{d}{d θ} (v (x, θ)) cos (θ) + (- sin (θ)) v (x, θ)))

e x p an d 2 x y^{3} d x + 3 (x^{2} + 1) y^{2} d y

e x p an d A (3, 4) - B (1, - 1) - C (- 5, 3)

e x p an d (1 - y) y^{'} (t) + 2 y

s l o p e (- 4, - 10), (- 3, - 7)

e x p an d \frac{( x + 6 ) ( x + 5 )}{2}