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Beliebt Rechnen >

derivative of 6x^3cos(x)

Lösung

\frac{d}{d x} (6 x^{3} cos (x))

Lösung

6 (3 x^{2} cos (x) - x^{3} sin (x))

Schritte zur Lösung

\frac{d}{d x} (6 x^{3} cos (x))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{3} cos (x))

Wende die Produktregel an:

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

f = x^{3}, g = cos (x)

= 6 (\frac{d}{d x} (x^{3}) cos (x) + \frac{d}{d x} (cos (x)) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 6 (3 x^{2} cos (x) + (- sin (x)) x^{3})

Vereinfache

= 6 (3 x^{2} cos (x) - x^{3} sin (x))

Graph

Beliebte Beispiele

4 x y^{^{'}} + 2 y = 10 x^{6}

integral of (x^3+x^2)/(x^5)

\int \frac{x ^{3} + x ^{2}}{x ^{5}} d x

derivative (x^4-3x)^2

d er i v a t i v e (x^{4} - 3 x)^{2}

d er i v a t i v e 13 x

integral of (2x)/(e^{8x)}

\int \frac{2 x}{e ^{8 x}} d x