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Beliebt Rechnen >

derivative of x^{sqrt(x)+1}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

x^{x + 1} = e^{(x + 1) l n (x)}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of-e^{-xy}

\frac{d}{d x} (- e^{- x y})

integral from 1 to infinity of (e^{-x})

\int_{1}^{\infty} (e^{- x}) d x

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\int \frac{6}{x - 1} d x

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\int 3 x + 2 d x