de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative f(x)=(x^3+1)*3x^2

Lösung

ableitung von

f (x) = (x^{3} + 1) \cdot 3 x^{2}

Lösung

3 (5 x^{4} + 2 x)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 1) \cdot 3 x^{2})

Entferne die Konstante:

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

= 3 \frac{d}{d x} ((x^{3} + 1) x^{2})

Wende die Produktregel an:

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

f = x^{3} + 1, g = x^{2}

= 3 (\frac{d}{d x} (x^{3} + 1) x^{2} + \frac{d}{d x} (x^{2}) (x^{3} + 1))

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

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

= 3 (3 x^{2} x^{2} + 2 x (x^{3} + 1))

Vereinfache

3 (3 x^{2} x^{2} + 2 x (x^{3} + 1)) : 3 (5 x^{4} + 2 x)

= 3 (5 x^{4} + 2 x)

Graph

Beliebte Beispiele

laplacetransform tsin(9t)

l a pl a ce t r an s f or m t sin (9 t)

fläche y=x^2-x,y=0

a re a y = x^{2} - x, y = 0

inverselaplace (2s+9)/(s^2+4s+40)

in v erse l a pl a ce \frac{2 s + 9}{s ^{2} + 4 s + 40}

(\partial)/(\partial t)(t/(c^2t^2-x^2))

\frac{\partial}{\partial t} (\frac{t}{c ^{2} t ^{2} - x ^{2}})

y^{''}+12y^'+36=0

y^{^{''}} + 12 y^{^{'}} + 36 = 0