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Beliebt Rechnen >

derivative 3^{x^5}

Lösung

ableitung von

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-14)/(x^2(x+2))

\int \frac{x - 14}{x ^{2} ( x + 2 )} d x

derivative f(x)= 4/(x+4)

d er i v a t i v e f (x) = \frac{4}{x + 4}

integral from 2 to x of t^5

\int_{2}^{x} t^{5} d t

derivative f(x)=cot(x)tan(x)

d er i v a t i v e f (x) = cot (x) tan (x)

x (x + 1) y^{^{'}} + x y = 1