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Beliebt Rechnen >

d/(dt)(cos(t)(1-sin(t)))

Lösung

\frac{d}{d t} (cos (t) (1 - sin (t)))

Lösung

- sin (t) (1 - sin (t)) - cos^{2} (t)

Schritte zur Lösung

\frac{d}{d t} (cos (t) (1 - sin (t)))

Wende die Produktregel an:

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

f = cos (t), g = 1 - sin (t)

= \frac{d}{d t} (cos (t)) (1 - sin (t)) + \frac{d}{d t} (1 - sin (t)) cos (t)

\frac{d}{d t} (cos (t)) = - sin (t)

\frac{d}{d t} (1 - sin (t)) = - cos (t)

= (- sin (t)) (1 - sin (t)) + (- cos (t)) cos (t)

Vereinfache

(- sin (t)) (1 - sin (t)) + (- cos (t)) cos (t) : - sin (t) (1 - sin (t)) - cos^{2} (t)

= - sin (t) (1 - sin (t)) - cos^{2} (t)

Graph

Beliebte Beispiele

integral from 0 to 2 of 1/(x^4+1)

\int_{0}^{2} \frac{1}{x ^{4} + 1} d x

derivative 4xe^{x^2-1}

d er i v a t i v e 4 x e^{x^{2} - 1}

derivative f(x)= 2/(3x)-1/(6sqrt(x))

d er i v a t i v e f (x) = \frac{2}{3 x} - \frac{1}{6 x}

taylor sin(x),pi

t a y l or sin (x), π

(dP)/(dt)=P(850-P)

\frac{d P}{d t} = P (850 - P)