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Beliebt Rechnen >

derivative of 8ysin(x)

Lösung

\frac{d}{d x} (8 y sin (x))

Lösung

8 (\frac{d y}{d x} sin (x) + cos (x) y)

Schritte zur Lösung

\frac{d}{d x} (8 y sin (x))

Entferne die Konstante:

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

= 8 \frac{d}{d x} (y sin (x))

Wende die Produktregel an:

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

f = y, g = sin (x)

= 8 (\frac{d y}{d x} sin (x) + \frac{d}{d x} (sin (x)) y)

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

= 8 (\frac{d y}{d x} sin (x) + cos (x) y)

Beliebte Beispiele

taylor cos(x),pi

t a y l or cos (x), π

integral of 8x^3(2x^4+4)

\int 8 x^{3} (2 x^{4} + 4) d x

derivative of cos(x-1/2)

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

integral from 0 to 1 of xe^{3x}

\int_{0}^{1} x e^{3 x} d x

integral of 9x(1-x)

\int 9 x (1 - x) d x