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Beliebt Rechnen >

derivative of 2x^{sqrt(x)}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{x} = e^{x l n (x)}

= 2 \frac{d}{d x} (e^{x l n (x)})

Wende die Kettenregel an:

e^{x l n (x)} \frac{d}{d x} (x ln (x))

= e^{x l n (x)} \frac{d}{d x} (x ln (x))

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

= 2 e^{x l n (x)} (\frac{ln ( x )}{2 x} + \frac{1}{x})

Vereinfache

2 e^{x l n (x)} (\frac{ln ( x )}{2 x} + \frac{1}{x}) : x^{\frac{2 x - 1}{2}} ln (x) + 2 x^{\frac{2 x - 1}{2}}

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

Graph

Beliebte Beispiele

integral of (sqrt(2x-3))/(2x+1)

\int \frac{2 x - 3}{2 x + 1} d x

integral of-4sin(5x)sin(x)

\int - 4 sin (5 x) sin (x) d x

derivative of 1/(1+sin(x))

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

integral of 3/4 t+6

\int \frac{3}{4} t + 6 d t

limit as x approaches 3-of sqrt(9-x^2)

x \to 3 - lim (9 - x^{2})