derivative y=log_{2}(x)*log_{5}(x)

Lösung

ableitung von

y = lo g_{2} (x) \cdot lo g_{5} (x)

\frac{2 ln ( x )}{ln ( 2 ) ln ( 5 ) x}

Schritte zur Lösung

\frac{d}{d x} (lo g_{2} (x) lo g_{5} (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = lo g_{2} (x), g = lo g_{5} (x)

= \frac{d}{d x} (lo g_{2} (x)) lo g_{5} (x) + \frac{d}{d x} (lo g_{5} (x)) lo g_{2} (x)

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

\frac{d}{d x} (lo g_{5} (x)) = \frac{1}{x ln ( 5 )}

= \frac{1}{x ln ( 2 )} lo g_{5} (x) + \frac{1}{x ln ( 5 )} lo g_{2} (x)

Vereinfache

\frac{1}{x ln ( 2 )} lo g_{5} (x) + \frac{1}{x ln ( 5 )} lo g_{2} (x) : \frac{2 ln ( x )}{ln ( 2 ) ln ( 5 ) x}

= \frac{2 ln ( x )}{ln ( 2 ) ln ( 5 ) x}

x \to 2 - lim (\frac{1}{x ^{2} - 4})

in v erse l a pl a ce \frac{e ^{- 4 s}}{( s + 2 ) ^{3}}

x \to 0 + lim (\frac{2 x}{x ^{2}})

\frac{d}{d x} (\frac{5 - 4 x ^{2} + x ^{5}}{x ^{3}})

\int \frac{36}{36 + e ^{x}} d x