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Beliebt Rechnen >

derivative of 2^{ln(x})

Lösung

\frac{d}{d 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

(d^3)/(dx^3)(2x^3-4)

\frac{d ^{3}}{d x ^{3}} (2 x^{3} - 4)

(\partial)/(\partial x)(e^{-2x}cos(9pit))

\frac{\partial}{\partial x} (e^{- 2 x} cos (9 π t))

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\frac{d}{d t} (2 cos (2 t))

derivative of x/(5x+8)

\frac{d}{d x} (\frac{x}{5 x + 8})

limit as x approaches-2+of (1-x)/(x+2)

x \to - 2 + lim (\frac{1 - x}{x + 2})