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Beliebt Rechnen >

derivative of log_{e}(ax)

Lösung

\frac{d}{d x} (lo g_{e} (a x))

Lösung

\frac{1}{x}

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (a x))

Vereinfache

lo g_{e} (a x) : ln (a x)

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

Wende die Kettenregel an:

\frac{1}{a x} \frac{d}{d x} (a x)

= \frac{1}{a x} \frac{d}{d x} (a x)

\frac{d}{d x} (a x) = a

= \frac{1}{a x} a

Vereinfache

\frac{1}{a x} a : \frac{1}{x}

= \frac{1}{x}

Graph

Beliebte Beispiele

integral of sec^3(3x)

\int sec^{3} (3 x) d x

derivative of 10^{3x}

\frac{d}{d x} (1 0^{3 x})

limit as x approaches 2 of x^2-3

x \to 2 lim (x^{2} - 3)

6x^2y^'=y^'+2xe^{-y}

6 x^{2} y^{^{'}} = y^{^{'}} + 2 x e^{- y}

(\partial)/(\partial x)(x^3cos(y))

\frac{\partial}{\partial x} (x^{3} cos (y))