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-6^4(x^2+x+1)^5)

Lösung

\frac{d}{d x} ((2 x - 6)^{4} (x^{2} + x + 1)^{5})

Lösung

8 (2 x - 6)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 6)^{4}

Schritte zur Lösung

\frac{d}{d x} ((2 x - 6)^{4} (x^{2} + x + 1)^{5})

Wende die Produktregel an:

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

f = (2 x - 6)^{4}, g = (x^{2} + x + 1)^{5}

= \frac{d}{d x} ((2 x - 6)^{4}) (x^{2} + x + 1)^{5} + \frac{d}{d x} ((x^{2} + x + 1)^{5}) (2 x - 6)^{4}

\frac{d}{d x} ((2 x - 6)^{4}) = 8 (2 x - 6)^{3}

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

= 8 (2 x - 6)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 6)^{4}

Graph

Beliebte Beispiele

integral of (t+1)^2

\int (t + 1)^{2} d t

integral from 1 to 4 of (5x+sqrt(x))

\int_{1}^{4} (5 x + x) d x

integral of x(arctan(x))^2

\int x (arctan (x))^{2} d x

integral of (tan(x))/(cos^3(x))

\int \frac{tan ( x )}{cos ^{3} ( x )} d x

(dy)/(y^2-4)=dx

\frac{d y}{y ^{2} - 4} = d x