derivative of log_{2}((x-1^3))

Lösung

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

\frac{3}{ln ( 2 ) ( x - 1 )}

Schritte zur Lösung

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

Wende die log Regel an:

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

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e f (x) = x \cdot e^{- x + 1}

t an g e n t 4 + 5 x^{2} - 2 x^{3}

\frac{d}{d x} (\frac{sin ( x ) + cos ( x )}{e ^{x}})

x \to 5 - lim (8 - x - x^{2})

y^{^{'}} = \frac{x - 2}{y - 2}