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Beliebt Rechnen >

derivative of (5x^3^x)

Lösung

\frac{d}{d x} ((5 x^{3})^{x})

Lösung

(ln (5 x^{3}) + 3) (5 x^{3})^{x}

Schritte zur Lösung

\frac{d}{d x} ((5 x^{3})^{x})

Wende Exponentenregel an:

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

(5 x^{3})^{x} = e^{x l n (5 x^{3})}

= \frac{d}{d x} (e^{x l n (5 x^{3})})

Wende die Kettenregel an:

e^{x l n (5 x^{3})} \frac{d}{d x} (x ln (5 x^{3}))

= e^{x l n (5 x^{3})} \frac{d}{d x} (x ln (5 x^{3}))

\frac{d}{d x} (x ln (5 x^{3})) = ln (5 x^{3}) + 3

= e^{x l n (5 x^{3})} (ln (5 x^{3}) + 3)

e^{x l n (5 x^{3})} = (5 x^{3})^{x}

= (ln (5 x^{3}) + 3) (5 x^{3})^{x}

Graph

Beliebte Beispiele

x(dy)/(dx)+y=3xy

x \frac{d y}{d x} + y = 3 x y

integral of ln(9)

\int ln (9) d x

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\frac{\partial}{\partial t} (9 cos (t))

derivative of (x^3ln(x)/(x+2))

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