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^2sqrt(1-x^2)

Lösung

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

Lösung

\frac{- 3 x ^{3} + 2 x}{1 - x ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = 1 - x^{2}

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

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

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

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

Vereinfache

2 x 1 - x^{2} + (- \frac{x}{1 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 2 x}{1 - x ^{2}}

= \frac{- 3 x ^{3} + 2 x}{1 - x ^{2}}

Graph

Beliebte Beispiele

integral of (x^4+\sqrt[3]{x}+3x)/(5x^3)

derivative of-8ln(x)

derivative y=7x^{-7}

(3x+2y+2y^2)dx+(x+2xy)dy=0

d/(dt)(k^2sin^2(t))