d/(dθ)(sin(θ)(4cos(θ)-4))

Lösung

\frac{d}{d θ} (sin (θ) (4 cos (θ) - 4))

cos (θ) (4 cos (θ) - 4) - 4 sin^{2} (θ)

Schritte zur Lösung

\frac{d}{d θ} (sin (θ) (4 cos (θ) - 4))

Wende die Produktregel an:

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

f = sin (θ), g = 4 cos (θ) - 4

= \frac{d}{d θ} (sin (θ)) (4 cos (θ) - 4) + \frac{d}{d θ} (4 cos (θ) - 4) sin (θ)

\frac{d}{d θ} (sin (θ)) = cos (θ)

\frac{d}{d θ} (4 cos (θ) - 4) = - 4 sin (θ)

= cos (θ) (4 cos (θ) - 4) + (- 4 sin (θ)) sin (θ)

Vereinfache

cos (θ) (4 cos (θ) - 4) + (- 4 sin (θ)) sin (θ) : cos (θ) (4 cos (θ) - 4) - 4 sin^{2} (θ)

= cos (θ) (4 cos (θ) - 4) - 4 sin^{2} (θ)

x \to 0 lim (ln^{2} (x))

\int_{0}^{5} \frac{x ^{3}}{x ^{4} + 4} d x

\frac{d}{d x} ((x - 8)^{2})

a re a 3 x^{2}, \frac{1}{3} x, 0, 0.5

d er i v a t i v e f (x) = \frac{x ^{2} - 6 x}{x + 1}