de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

6 (3 x - 3) (1 - 5 x)^{4} - 20 (1 - 5 x)^{3} (3 x - 3)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((1 - 5 x)^{4}) = - 20 (1 - 5 x)^{3}

= 6 (3 x - 3) (1 - 5 x)^{4} + (- 20 (1 - 5 x)^{3}) (3 x - 3)^{2}

Vereinfache

= 6 (3 x - 3) (1 - 5 x)^{4} - 20 (1 - 5 x)^{3} (3 x - 3)^{2}

Graph

Beliebte Beispiele

y^{^{''}} + 2 y + y = 0

tangent f(x)=(5/(x^2+1)),\at x=-1

t an g e n t f (x) = (\frac{5}{x ^{2} + 1}), at x = - 1

y^'=2e^{(6x-y)}

y^{^{'}} = 2 e^{(6 x - y)}

integral of (x^2+x)e^{2x}

\int (x^{2} + x) e^{2 x} d x

(\partial)/(\partial z)(2yz)

\frac{\partial}{\partial z} (2 yz)