de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative y=2x^2sqrt(2-x)

Lösung

ableitung von

y = 2 x^{2} 2 - x

Lösung

\frac{- 5 x ^{2} + 8 x}{2 - x}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x^{2}, g = 2 - x

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

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

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

= 2 (2 x 2 - x + (- \frac{1}{2 2 - x}) x^{2})

Vereinfache

2 (2 x 2 - x + (- \frac{1}{2 2 - x}) x^{2}) : \frac{- 5 x ^{2} + 8 x}{2 - x}

= \frac{- 5 x ^{2} + 8 x}{2 - x}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(e^{-1}cos(pix))

\frac{\partial}{\partial x} (e^{- 1} cos (π x))

(dx}{dt}=\frac{2x)/t ,x(3)=1

\frac{d x}{d t} = \frac{2 x}{t}, x (3) = 1

laplacetransform 10+t^2

l a pl a ce t r an s f or m 10 + t^{2}

integral from 0 to pi of sin^2(7x)

\int_{0}^{π} sin^{2} (7 x) d x

integral of-sec^2(x)

\int - sec^{2} (x) d x