de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative (2x-3)^4(x^2+x+1)^5

Lösung

ableitung von

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

Lösung

8 (2 x - 3)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 3)^{4}

Schritte zur Lösung

\frac{d}{d x} ((2 x - 3)^{4} (x^{2} + x + 1)^{5})

Wende die Produktregel an:

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

f = (2 x - 3)^{4}, g = (x^{2} + x + 1)^{5}

= \frac{d}{d x} ((2 x - 3)^{4}) (x^{2} + x + 1)^{5} + \frac{d}{d x} ((x^{2} + x + 1)^{5}) (2 x - 3)^{4}

\frac{d}{d x} ((2 x - 3)^{4}) = 8 (2 x - 3)^{3}

\frac{d}{d x} ((x^{2} + x + 1)^{5}) = 5 (x^{2} + x + 1)^{4} (2 x + 1)

= 8 (2 x - 3)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 3)^{4}

Graph

Beliebte Beispiele

\frac{d}{d t} (A t e^{t})

derivative of (-6x/(sqrt(2x-1)))

\frac{d}{d x} (\frac{- 6 x}{2 x - 1})

derivative (4x^5+7)/(x^3)

d er i v a t i v e \frac{4 x ^{5} + 7}{x ^{3}}

derivative of ln((x^2+1/(x+4)))

\frac{d}{d x} (ln (\frac{x ^{2} + 1}{x + 4}))

integral of e^{7x+9}

\int e^{7 x + 9} d x