de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative y=x^3(2x-5)^4

Lösung

ableitung von

y = x^{3} (2 x - 5)^{4}

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((2 x - 5)^{4}) = 8 (2 x - 5)^{3}

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

Graph

Beliebte Beispiele

-e^xy(dy)/(dx)=e^{-y}+e^{-2x-y}

- e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

integral of (x^2)/((1+x^2)^2)

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

derivative of-(sin(ln(x))/x)

\frac{d}{d x} (- \frac{sin ( ln ( x ) )}{x})

derivative of-x^2y

\frac{d}{d x} (- x^{2} y)

derivative sqrt(3-6x)

d er i v a t i v e 3 - 6 x