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Beliebt Rechnen >

derivative f(x)=2^{ln(x)}

Lösung

ableitung von

f (x) = 2^{l n (x)}

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

2^{l n (x)} = e^{l n (x) l n (2)}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

fläche 6x^2-9x-6,7x^2-5x-3

a re a 6 x^{2} - 9 x - 6, 7 x^{2} - 5 x - 3

limit as x approaches 0 of x/5

x \to 0 lim (\frac{x}{5})

derivative (x^2-9)^2+2

d er i v a t i v e (x^{2} - 9)^{2} + 2

7x(x+3y)y^'=7y(x-3y)

7 x (x + 3 y) y^{^{'}} = 7 y (x - 3 y)

5(dr)/(ds)=e^{r-8s}

5 \frac{d r}{d s} = e^{r - 8 s}