de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 2xsqrt(25-x^2)

Lösung

\frac{d}{d x} (2 x 25 - x^{2})

Lösung

\frac{2 ( - 2 x ^{2} + 25 )}{25 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x 25 - x^{2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x 25 - x^{2})

Wende die Produktregel an:

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

f = x, g = 25 - x^{2}

= 2 (\frac{d x}{d x} 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 2 (1 \cdot 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x)

Vereinfache

2 (1 \cdot 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x) : \frac{2 ( - 2 x ^{2} + 25 )}{25 - x ^{2}}

= \frac{2 ( - 2 x ^{2} + 25 )}{25 - x ^{2}}

Graph

Beliebte Beispiele

integral of (x^5e^{x^6})

\int (x^{5} e^{x^{6}}) d x

integral of x^3-2x+3

\int x^{3} - 2 x + 3 d x

(\partial)/(\partial x)(9x)

\frac{\partial}{\partial x} (9 x)

limit as x approaches 4 of x^3

x \to 4 lim (x^{3})

limit as x approaches-2 of ((3))/(x+2)

x \to - 2 lim (\frac{( 3 )}{x + 2})