de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of (x+2(3x^2-4)^2)

Lösung

\frac{d}{d x} ((x + 2) (3 x^{2} - 4)^{2})

Lösung

45 x^{4} + 72 x^{3} - 72 x^{2} - 96 x + 16

Schritte zur Lösung

\frac{d}{d x} ((x + 2) (3 x^{2} - 4)^{2})

Wende die Produktregel an:

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

f = x + 2, g = (3 x^{2} - 4)^{2}

= \frac{d}{d x} (x + 2) (3 x^{2} - 4)^{2} + \frac{d}{d x} ((3 x^{2} - 4)^{2}) (x + 2)

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

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

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

Vereinfache

1 \cdot (3 x^{2} - 4)^{2} + 12 x (3 x^{2} - 4) (x + 2) : 45 x^{4} + 72 x^{3} - 72 x^{2} - 96 x + 16

= 45 x^{4} + 72 x^{3} - 72 x^{2} - 96 x + 16

Graph

Beliebte Beispiele

derivative of cos(3x3)

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

y^{''}-8y^'+9y=xe^x

y^{^{''}} - 8 y^{^{'}} + 9 y = x e^{x}

laplacetransform sin(2(t-pi/2))

l a pl a ce t r an s f or m sin (2 (t - \frac{π}{2}))

fläche x^2-4x,x-4

a re a x^{2} - 4 x, x - 4

integral of sin(9pix)

\int sin (9 π x) d x