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Beliebt Rechnen >

derivative of 4xcos(x)

Lösung

\frac{d}{d x} (4 x cos (x))

Lösung

4 (cos (x) - x sin (x))

Schritte zur Lösung

\frac{d}{d x} (4 x cos (x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x cos (x))

Wende die Produktregel an:

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

f = x, g = cos (x)

= 4 (\frac{d x}{d x} cos (x) + \frac{d}{d x} (cos (x)) x)

\frac{d x}{d x} = 1

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

= 4 (1 \cdot cos (x) + (- sin (x)) x)

Vereinfache

= 4 (cos (x) - x sin (x))

Graph

Beliebte Beispiele

derivative of 2/3 x^{-1/3}

\frac{d}{d x} (\frac{2}{3} x^{- \frac{1}{3}})

integral of (x/y)

\int (\frac{x}{y}) d y

integral from 4 to infinity of e^{4x}

\int_{4}^{\infty} e^{4 x} d x

integral of sqrt(5-x^2)

\int 5 - x^{2} d x

integral of x^3*sqrt(1-x^2)

\int x^{3} \cdot 1 - x^{2} d x