derivative of log_{2}(2x^2-7x+1)

Lösung

\frac{d}{d x} (lo g_{2} (2 x^{2} - 7 x + 1))

\frac{4 x - 7}{ln ( 2 ) ( 2 x ^{2} - 7 x + 1 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{2} (2 x^{2} - 7 x + 1))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( 2 x ^{2} - 7 x + 1 )}{ln ( 2 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 2 )} \frac{d}{d x} (ln (2 x^{2} - 7 x + 1))

Wende die Kettenregel an:

\frac{1}{2 x ^{2} - 7 x + 1} \frac{d}{d x} (2 x^{2} - 7 x + 1)

= \frac{1}{2 x ^{2} - 7 x + 1} \frac{d}{d x} (2 x^{2} - 7 x + 1)

\frac{d}{d x} (2 x^{2} - 7 x + 1) = 4 x - 7

= \frac{1}{ln ( 2 )} \cdot \frac{1}{2 x ^{2} - 7 x + 1} (4 x - 7)

Vereinfache

\frac{1}{ln ( 2 )} \cdot \frac{1}{2 x ^{2} - 7 x + 1} (4 x - 7) : \frac{4 x - 7}{ln ( 2 ) ( 2 x ^{2} - 7 x + 1 )}

= \frac{4 x - 7}{ln ( 2 ) ( 2 x ^{2} - 7 x + 1 )}

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