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^3(x-8^2)

Lösung

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

Lösung

5 x^{4} - 64 x^{3} + 192 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = (x - 8)^{2}

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

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

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

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

Vereinfache

3 x^{2} (x - 8)^{2} + 2 (x - 8) x^{3} : 5 x^{4} - 64 x^{3} + 192 x^{2}

= 5 x^{4} - 64 x^{3} + 192 x^{2}

Graph

Beliebte Beispiele

derivative of 1/(x-y)

\frac{d}{d x} (\frac{1}{x - y})

(dy)/(dx)+1/x y=0

\frac{d y}{d x} + \frac{1}{x} y = 0

integral of 2cos(x/3)

\int 2 cos (\frac{x}{3}) d x

derivative f(x)=x^2-6x-7

d er i v a t i v e f (x) = x^{2} - 6 x - 7

xy^2y^'=y^3-5x^3

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}