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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

derivative of cos(xx^{-2})

(\partial}{\partial x}(\frac{3y^2)/x)

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