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Beliebt Rechnen >

derivative x^{3^x}

Lösung

ableitung von

x^{3^{x}}

Lösung

x^{3^{x}} (ln (3) \cdot 3^{x} ln (x) + \frac{3 ^{x}}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{3^{x}})

Wende Exponentenregel an:

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

x^{3^{x}} = e^{3^{x} l n (x)}

= \frac{d}{d x} (e^{3^{x} l n (x)})

Wende die Kettenregel an:

e^{3^{x} l n (x)} \frac{d}{d x} (3^{x} ln (x))

= e^{3^{x} l n (x)} \frac{d}{d x} (3^{x} ln (x))

\frac{d}{d x} (3^{x} ln (x)) = ln (3) \cdot 3^{x} ln (x) + \frac{3 ^{x}}{x}

= e^{3^{x} l n (x)} (ln (3) \cdot 3^{x} ln (x) + \frac{3 ^{x}}{x})

e^{3^{x} l n (x)} = x^{3^{x}}

= x^{3^{x}} (ln (3) \cdot 3^{x} ln (x) + \frac{3 ^{x}}{x})

Graph

Beliebte Beispiele

integral of ((x+2)^2)/(x^2+4)

\int \frac{( x + 2 ) ^{2}}{x ^{2} + 4} d x

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\int \frac{x + 66}{x ^{2} - 36} d x

integral of (3x-4)^2

\int (3 x - 4)^{2} d x

derivative of csc(x^3)

\frac{d}{d x} (csc (x^{3}))

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