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Beliebt Rechnen >

d/(dy)(ycos(y))

Lösung

\frac{d}{d y} (y cos (y))

Lösung

cos (y) - y sin (y)

Schritte zur Lösung

\frac{d}{d y} (y cos (y))

Wende die Produktregel an:

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

f = y, g = cos (y)

= \frac{d y}{d y} cos (y) + \frac{d}{d y} (cos (y)) y

\frac{d y}{d y} = 1

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

= 1 \cdot cos (y) + (- sin (y)) y

Vereinfache

= cos (y) - y sin (y)

Graph

Beliebte Beispiele

derivative f(x)=(x^2)/(x-6)

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

x*(dy)/(dx)+y=-6xy^2,y(1)=-7

x \cdot \frac{d y}{d x} + y = - 6 x y^{2}, y (1) = - 7

derivative of e^{(e^{x^2}})

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

integral of (e 1/t+2)/(t^2)

\int \frac{e \frac{1}{t} + 2}{t ^{2}} d t

limit as x approaches 6 of x/(x^2+1)

x \to 6 lim (\frac{x}{x ^{2} + 1})