de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 2x^2cos(4x)

Lösung

\frac{d}{d x} (2 x^{2} cos (4 x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (2 x^{2} cos (4 x))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x^{2} cos (4 x))

Wende die Produktregel an:

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

f = x^{2}, g = cos (4 x)

= 2 (\frac{d}{d x} (x^{2}) cos (4 x) + \frac{d}{d x} (cos (4 x)) x^{2})

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

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

Vereinfache

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

Graph

Beliebte Beispiele

limit as x approaches-1 of (2x+1)/(x-2)

x \to - 1 lim (\frac{2 x + 1}{x - 2})

tangent x^2+3x,\at x=0

t an g e n t x^{2} + 3 x, at x = 0

integral of-5ln(x^2-1)

\int - 5 ln (x^{2} - 1) d x

derivative f(x)=(2x^2+3)^3(x^2-4)^2

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

d/(dv)(ln(ucos(v)))

\frac{d}{d v} (ln (u cos (v)))