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(x^2+3^3)

Lösung

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

Lösung

(x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((x^{2} + 3)^{3}) = 6 x (x^{2} + 3)^{2}

= 1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x

Vereinfache

1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x : (x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}

= (x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}

Graph

Beliebte Beispiele

y^{''}+9y=2x^2-5

y^{^{''}} + 9 y = 2 x^{2} - 5

limit as x approaches 1 of (x^{10}-1)/(x-1)

x \to 1 lim (\frac{x ^{10} - 1}{x - 1})

derivative of-2/((1+2x^2))

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

derivative of sqrt(x)e^{2x}

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

limit as x approaches infinity of a^{-x}

x \to \infty lim (a^{- x})