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Beliebt Rechnen >

derivative of 10log_{10}(100x)

Lösung

\frac{d}{d x} (10 lo g_{10} (100 x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (10 lo g_{10} (100 x))

Vereinfache

10 lo g_{10} (100 x) : 10 (lo g_{10} (x) + 2)

= \frac{d}{d x} (10 (lo g_{10} (x) + 2))

Entferne die Konstante:

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

= 10 \frac{d}{d x} (lo g_{10} (x) + 2)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 10 (\frac{d}{d x} (lo g_{10} (x)) + \frac{d}{d x} (2))

\frac{d}{d x} (lo g_{10} (x)) = \frac{1}{x ln ( 10 )}

\frac{d}{d x} (2) = 0

= 10 (\frac{1}{x ln ( 10 )} + 0)

Vereinfache

10 (\frac{1}{x ln ( 10 )} + 0) : \frac{10}{ln ( 10 ) x}

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

Graph

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