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Beliebt Rechnen >

derivative of x*cos^3(4x)

Lösung

\frac{d}{d x} (x \cdot cos^{3} (4 x))

Lösung

cos^{3} (4 x) - 12 x cos^{2} (4 x) sin (4 x)

Schritte zur Lösung

\frac{d}{d x} (x cos^{3} (4 x))

Wende die Produktregel an:

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

f = x, g = cos^{3} (4 x)

= \frac{d x}{d x} cos^{3} (4 x) + \frac{d}{d x} (cos^{3} (4 x)) x

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

\frac{d}{d x} (cos^{3} (4 x)) = - 12 cos^{2} (4 x) sin (4 x)

= 1 \cdot cos^{3} (4 x) + (- 12 cos^{2} (4 x) sin (4 x)) x

Vereinfache

= cos^{3} (4 x) - 12 x cos^{2} (4 x) sin (4 x)

Graph

Beliebte Beispiele

derivative of x^4+e^{-x}

\frac{d}{d x} (x^{4} + e^{- x})

limit as x approaches 0 of 2x+4

x \to 0 lim (2 x + 4)

limit as x approaches 0 of 9x-6

x \to 0 lim (9 x - 6)

integral of-cos(x)+sin(x)+C

\int - cos (x) + sin (x) + C d x

(d^3x)/(dt^3)-3x=0

\frac{d ^{3} x}{d t ^{3}} - 3 x = 0