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Beliebt Rechnen >

derivative of e^{x^3ln(x})

Lösung

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

Lösung

x^{x^{3}} (3 x^{2} ln (x) + x^{2})

Schritte zur Lösung

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

Vereinfache

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

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{3} ln (x)) = 3 x^{2} ln (x) + x^{2}

= e^{x^{3} l n (x)} (3 x^{2} ln (x) + x^{2})

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

= x^{x^{3}} (3 x^{2} ln (x) + x^{2})

Graph

Beliebte Beispiele

(\partial)/(\partial x)(3x^2y^4+3)

\frac{\partial}{\partial x} (3 x^{2} y^{4} + 3)

f(x)=(cos(2x)ln(x))/(x-5)

f (x) = \frac{cos ( 2 x ) ln ( x )}{x - 5}

integral of x*e^{6x}

\int x \cdot e^{6 x} d x

fläche 2(x-1)^2+50,3(x+3)^2+2

a re a 2 (x - 1)^{2} + 50, 3 (x + 3)^{2} + 2

integral of x^2-5x

\int x^{2} - 5 x d x