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Beliebt Rechnen >

derivative of 4x*sin(x)

Lösung

\frac{d}{d x} (4 x \cdot sin (x))

Lösung

4 (sin (x) + x cos (x))

Schritte zur Lösung

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

Entferne die Konstante:

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

= 4 \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)

= 4 (\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)

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

Vereinfache

= 4 (sin (x) + x cos (x))

Graph

Beliebte Beispiele

integral of-sin(3x)

\int - sin (3 x) d x

derivative of (6-x^{-1})

\frac{d}{d x} ((6 - x)^{- 1})

integral of 1/(1+100x^2)

\int \frac{1}{1 + 100 x ^{2}} d x

y^{''}-4y^'-32y=0

y^{^{''}} - 4 y^{^{'}} - 32 y = 0

laplacetransform 2e^t+5

l a pl a ce t r an s f or m 2 e^{t} + 5