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Beliebt Rechnen >

(\partial)/(\partial θ)(r(θ)*sin(θ))

Lösung

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

Lösung

r (sin (θ) + θ cos (θ))

Schritte zur Lösung

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

Behandle

r

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = θ, g = sin (θ)

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

\frac{\partial}{\partial θ} (θ) = 1

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

= r (1 \cdot sin (θ) + cos (θ) θ)

Vereinfache

= r (sin (θ) + θ cos (θ))

Beliebte Beispiele

(\partial)/(\partial x)(xze^{xz})

\frac{\partial}{\partial x} (x z e^{x z})

derivative cos(sqrt(sin(tan(9x))))

d er i v a t i v e cos (sin (tan (9 x)))

tangent x^3+y^3-4xy=0,(2,2)

t an g e n t x^{3} + y^{3} - 4 x y = 0, (2, 2)

derivative G(t)=(1-4t)/(3+t)

d er i v a t i v e G (t) = \frac{1 - 4 t}{3 + t}

f(x)=(sin(x))/(x^2)

f (x) = \frac{sin ( x )}{x ^{2}}