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Beliebt Rechnen >

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

Lösung

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

Lösung

cos (2 t)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

cos (t) cos (t) + (- sin (t)) sin (t) : cos (2 t)

= cos (2 t)

Graph

Beliebte Beispiele

\frac{d y}{d x} = 2 y + 2

integral of sin(3x)sec^2(3x)

\int sin (3 x) sec^{2} (3 x) d x

(d^2)/(dx^2)(e^{-4x^2})

\frac{d ^{2}}{d x ^{2}} (e^{- 4 x^{2}})

(\partial)/(\partial y)((xy^2)/(x+y))

\frac{\partial}{\partial y} (\frac{x y ^{2}}{x + y})

derivative sec(4x)

d er i v a t i v e sec (4 x)