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Beliebt Rechnen >

derivative 7xsin(x)

Lösung

ableitung von

7 x sin (x)

Lösung

7 (sin (x) + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (7 x sin (x))

Entferne die Konstante:

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

= 7 \frac{d}{d x} (x sin (x))

Wende die Produktregel an:

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

f = x, g = sin (x)

= 7 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

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

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

= 7 (1 \cdot sin (x) + cos (x) x)

Vereinfache

= 7 (sin (x) + x cos (x))

Graph

Beliebte Beispiele

integral from 1 to 3 of 2x+3

\int_{1}^{3} 2 x + 3 d x

derivative of 1/(9x+1)

\frac{d}{d x} (\frac{1}{9 x + 1})

integral of sin^2(x/3)

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

derivative of-2x+1/x

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

integral of (5x^2+5x-4)

\int (5 x^{2} + 5 x - 4) d x