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Beliebt Rechnen >

derivative of log_{6}(x^2-3x)

Lösung

\frac{d}{d x} (lo g_{6} (x^{2} - 3 x))

Lösung

\frac{2 x - 3}{ln ( 6 ) ( x ^{2} - 3 x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{6} (x^{2} - 3 x))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( x ^{2} - 3 x )}{ln ( 6 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 6 )} \frac{d}{d x} (ln (x^{2} - 3 x))

Wende die Kettenregel an:

\frac{1}{x ^{2} - 3 x} \frac{d}{d x} (x^{2} - 3 x)

= \frac{1}{x ^{2} - 3 x} \frac{d}{d x} (x^{2} - 3 x)

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

= \frac{1}{ln ( 6 )} \cdot \frac{1}{x ^{2} - 3 x} (2 x - 3)

Vereinfache

\frac{1}{ln ( 6 )} \cdot \frac{1}{x ^{2} - 3 x} (2 x - 3) : \frac{2 x - 3}{ln ( 6 ) ( x ^{2} - 3 x )}

= \frac{2 x - 3}{ln ( 6 ) ( x ^{2} - 3 x )}

Graph

Beliebte Beispiele

derivative f(x)=-16x^{3/2}+6x^{1.7}+x

d er i v a t i v e f (x) = - 16 x^{\frac{3}{2}} + 6 x^{1.7} + x

derivative of (cos(x)^x)

\frac{d}{d x} ((cos (x))^{x})

tangent ((x-1))/(x+1)

t an g e n t \frac{( x - 1 )}{x + 1}

tangent-7x^4+11x^2-4

t an g e n t - 7 x^{4} + 11 x^{2} - 4

integral of (x^2)/((1+9x^2)^{3/2)}

\int \frac{x ^{2}}{( 1 + 9 x ^{2} ) ^{\frac{3}{2}}} d x