(\partial)/(\partial θ)(r(θ)*cos(θ))

Lösung

\frac{\partial}{\partial θ} (r (θ) \cdot cos (θ))

r (cos (θ) - θ sin (θ))

Schritte zur Lösung

\frac{\partial}{\partial θ} (r (θ) cos (θ))

Behandle

r

als Konstante

Entferne die Konstante:

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

= r \frac{\partial}{\partial θ} (θ cos (θ))

Wende die Produktregel an:

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

f = θ, g = cos (θ)

= r (\frac{\partial}{\partial θ} (θ) cos (θ) + \frac{\partial}{\partial θ} (cos (θ)) θ)

\frac{\partial}{\partial θ} (θ) = 1

\frac{\partial}{\partial θ} (cos (θ)) = - sin (θ)

= r (1 \cdot cos (θ) + (- sin (θ)) θ)

Vereinfache

= r (cos (θ) - θ sin (θ))

d er i v a t i v e e^{r t}

\int_{- π}^{π} sin^{3} (x) d x

x \to 0 + lim (x ln (tan (3 x)))

d er i v a t i v e - \frac{19}{( 2 x - 5 ) ^{2}}

x \to - 26.8 lim (- 26.8)