derivative (log_{10}(x))/(x^2)

Lösung

ableitung von

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

\frac{1 - 2 ln ( x )}{ln ( 10 ) x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{\frac{1}{x l n ( 10 )} x ^{2} - 2 x lo g _{10} ( x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( x )}{ln ( 10 ) x ^{3}}

= \frac{1 - 2 ln ( x )}{ln ( 10 ) x ^{3}}

d er i v a t i v e 3 + 4 x^{2}

\frac{d}{d t} (a sin (t) + 1)

d er i v a t i v e 3 cos^{- 3} (x)

d er i v a t i v e (5 x^{9} + 7 x^{2} - 65)^{- 9}

d er i v a t i v e \frac{100}{x ^{2}}