de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative y=2\sqrt[4]{9-x^2}

Lösung

ableitung von

y = 2 4 9 - x^{2}

Lösung

- \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (2 4 9 - x^{2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (4 9 - x^{2})

Wende die Kettenregel an:

\frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (9 - x^{2})

= \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (9 - x^{2})

\frac{d}{d x} (9 - x^{2}) = - 2 x

= 2 \cdot \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x)

Vereinfache

2 \cdot \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x) : - \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

= - \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

Graph

Beliebte Beispiele

limit as x approaches 0 of-1+2

x \to 0 lim (- 1 + 2)

integral of 6x^2sqrt(2x^3+1)

\int 6 x^{2} 2 x^{3} + 1 d x

(dy)/(dt)=4y,y(5)=9

\frac{d y}{d t} = 4 y, y (5) = 9

integral of (x+7)/(x^2+16)

\int \frac{x + 7}{x ^{2} + 16} d x

limit as x approaches-4 of 1/(sqrt(x+4))

x \to - 4 lim (\frac{1}{x + 4})