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Beliebt Rechnen >

(\partial)/(\partial x)(log_{10}(x+1))

Lösung

\frac{\partial}{\partial x} (lo g_{10} (x + 1))

Lösung

\frac{1}{ln ( 10 ) ( x + 1 )}

Schritte zur Lösung

\frac{\partial}{\partial x} (lo g_{10} (x + 1))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{\partial}{\partial x} (\frac{ln ( x + 1 )}{ln ( 10 )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \frac{\partial}{\partial x} (ln (x + 1))

Wende die Kettenregel an:

\frac{1}{x + 1} \frac{\partial}{\partial x} (x + 1)

= \frac{1}{x + 1} \frac{\partial}{\partial x} (x + 1)

\frac{\partial}{\partial x} (x + 1) = 1

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x + 1} \cdot 1

Vereinfache

\frac{1}{ln ( 10 )} \cdot \frac{1}{x + 1} \cdot 1 : \frac{1}{ln ( 10 ) ( x + 1 )}

= \frac{1}{ln ( 10 ) ( x + 1 )}

Beliebte Beispiele

limit as x approaches 4 of (5x)/(x-4)

x \to 4 lim (\frac{5 x}{x - 4})

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\frac{d}{d x} (c x e^{2 x})

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

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

inverselaplace (s+5)/((s+3)(s-1))

in v erse l a pl a ce \frac{s + 5}{( s + 3 ) ( s - 1 )}

(\partial)/(\partial s)(re^s)

\frac{\partial}{\partial s} (r e^{s})