derivative of x/(log_{10(x)})

Lösung

\frac{d}{d x} (\frac{x}{lo g _{10} ( x )})

\frac{ln ( x ) - 1}{ln ( 10 ) lo g _{10} ( x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{lo g _{10} ( x )})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} lo g _{10} ( x ) - \frac{d}{d x} ( lo g _{10} ( x ) ) x}{( lo g _{10} ( x ) ) ^{2}}

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

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

= \frac{1 \cdot lo g _{10} ( x ) - \frac{1}{x l n ( 10 )} x}{( lo g _{10} ( x ) ) ^{2}}

Vereinfache

\frac{1 \cdot lo g _{10} ( x ) - \frac{1}{x l n ( 10 )} x}{lo g _{10} ( x ) ^{2}} : \frac{ln ( x ) - 1}{ln ( 10 ) lo g _{10} ( x ) ^{2}}

= \frac{ln ( x ) - 1}{ln ( 10 ) lo g _{10} ( x ) ^{2}}

d er i v a t i v e y = \frac{1}{lo g _{4} ( x )}

\int_{0}^{4} \frac{2}{x ^{2}} d x

\int_{- 1}^{1} 2 x^{2} d x

\frac{d}{d x} (\frac{- 20}{( 2 + x ) ^{2}})

a re a x^{2} - 11, 10 x