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Beliebt Rechnen >

derivative of (log_{2}(x)/x)

Lösung

\frac{d}{d x} (\frac{lo g _{2} ( x )}{x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{lo g _{2} ( x )}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( lo g _{2} ( x ) ) x - \frac{d x}{d x} lo g _{2} ( x )}{x ^{2}}

\frac{d}{d x} (lo g_{2} (x)) = \frac{1}{x ln ( 2 )}

\frac{d x}{d x} = 1

= \frac{\frac{1}{x l n ( 2 )} x - 1 \cdot lo g _{2} ( x )}{x ^{2}}

Vereinfache

\frac{\frac{1}{x l n ( 2 )} x - 1 \cdot lo g _{2} ( x )}{x ^{2}} : \frac{1 - ln ( x )}{ln ( 2 ) x ^{2}}

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

Graph

Beliebte Beispiele

derivative (x^2)/(x-4)

d er i v a t i v e \frac{x ^{2}}{x - 4}

tangent y=x^2+3,(-2,7)

t an g e n t y = x^{2} + 3, (- 2, 7)

integral from 0 to pi/2 of 45cos^5(x)

\int_{0}^{\frac{π}{2}} 45 cos^{5} (x) d x

derivative f(x)=2x+4x^{-1}

d er i v a t i v e f (x) = 2 x + 4 x^{- 1}

f (x) = 4 x e^{x}