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Beliebt Rechnen >

derivative of \sqrt[x]{2}

Lösung

\frac{d}{d x} (x 2)

Lösung

- \frac{ln ( 2 ) \cdot 2 ^{\frac{1}{x}}}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x 2)

Wende Exponentenregel an:

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

x 2 = e^{\frac{1}{x} l n (2)}

= \frac{d}{d x} (e^{\frac{1}{x} l n (2)})

Wende die Kettenregel an:

e^{\frac{1}{x} l n (2)} \frac{d}{d x} (\frac{1}{x} ln (2))

= e^{\frac{1}{x} l n (2)} \frac{d}{d x} (\frac{1}{x} ln (2))

\frac{d}{d x} (\frac{1}{x} ln (2)) = - \frac{ln ( 2 )}{x ^{2}}

= e^{\frac{1}{x} l n (2)} (- \frac{ln ( 2 )}{x ^{2}})

Vereinfache

e^{\frac{1}{x} l n (2)} (- \frac{ln ( 2 )}{x ^{2}}) : - \frac{ln ( 2 ) \cdot 2 ^{\frac{1}{x}}}{x ^{2}}

= - \frac{ln ( 2 ) \cdot 2 ^{\frac{1}{x}}}{x ^{2}}

Graph

Beliebte Beispiele

integral of x-x^4

\int x - x^{4} d x

sum from n=0 to infinity of 2^{-2n}

n = 0 \sum \infty 2^{- 2 n}

limit as x approaches 0 of 4^2

x \to 0 lim (4^{2})

derivative of (36/x)

\frac{d}{d x} (\frac{36}{x})

inverselaplace (3s+4)/(s^2-1)

in v erse l a pl a ce \frac{3 s + 4}{s ^{2} - 1}