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Beliebt Rechnen >

derivative of 2sqrt(1+x)

Lösung

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

Lösung

\frac{1}{1 + x}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (1 + x) = 1

= 2 \cdot \frac{1}{2 1 + x} \cdot 1

Vereinfache

2 \cdot \frac{1}{2 1 + x} \cdot 1 : \frac{1}{1 + x}

= \frac{1}{1 + x}

Graph

Beliebte Beispiele

derivative f(x)=(x+1)^2

d er i v a t i v e f (x) = (x + 1)^{2}

y^{''}+324y=sec(18x)

y^{^{''}} + 324 y = sec (18 x)

limit as x approaches 18 of (x^2)/2-9/x

x \to 18 lim (\frac{x ^{2}}{2} - \frac{9}{x})

y^'=2(3x+y)^2-1

y^{^{'}} = 2 (3 x + y)^{2} - 1

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

\int_{1}^{2} \frac{x + 2 x ^{2}}{x} d x