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Beliebt Rechnen >

derivative f(x)=3^{(x^5)}

Lösung

ableitung von

f (x) = 3^{(x^{5})}

Lösung

5 ln (3) \cdot 3^{x^{5}} x^{4}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{5} ln (3)) = 5 ln (3) x^{4}

= e^{x^{5} l n (3)} \cdot 5 ln (3) x^{4}

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

= 5 ln (3) \cdot 3^{x^{5}} x^{4}

Graph

Beliebte Beispiele

integral of (x^2)/(sqrt((2-x^2)))

(x)^2y^{''}+3(x)y^'-3y=(x)^3

derivative 1/(t^2)

integral from 0 to 1 of x*e^x