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Beliebt Rechnen >

derivative θcos(θ)sin(θ)

Lösung

ableitung von

θ cos (θ) sin (θ)

Lösung

cos (θ) sin (θ) + θ cos (2 θ)

Schritte zur Lösung

\frac{d}{d θ} (θ cos (θ) sin (θ))

Wende die Produktregel an:

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

f = θ, g = cos (θ) sin (θ)

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

\frac{d θ}{d θ} = 1

\frac{d}{d θ} (cos (θ) sin (θ)) = cos (2 θ)

= 1 \cdot cos (θ) sin (θ) + cos (2 θ) θ

Vereinfache

= cos (θ) sin (θ) + θ cos (2 θ)

Graph

Beliebte Beispiele

x^2(dy)/(dx)-y^3=xy

x^{2} \frac{d y}{d x} - y^{3} = x y

derivative of x/(1-x^2)

\frac{d}{d x} (\frac{x}{1 - x ^{2}})

integral of (x^2)/(x^3-3)

\int \frac{x ^{2}}{x ^{3} - 3} d x

integral from 0 to 5 of 0.2x

\int_{0}^{5} 0.2 x d x

sum from n=1 to infinity of n(n+1)

n = 1 \sum \infty n (n + 1)