(\partial)/(\partial θ)(r(θ)cos(θ))

Lösung

\frac{\partial}{\partial θ} (r (θ) 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))

\int sin (9 π) t d t

\frac{\partial}{\partial x} (\frac{4 x - 2 y}{4 x + 2 y})

\int \frac{1}{( x + 2 ) ^{\frac{3}{2}}} d x

x \to 5 lim (x^{2} + 4)

\int_{0}^{π} \frac{sin ( x )}{x} d x