derivative of xlog_{10}(2/x)

Lösung

\frac{d}{d x} (x lo g_{10} (\frac{2}{x}))

lo g_{10} (\frac{2}{x}) - \frac{1}{ln ( 10 )}

Schritte zur Lösung

\frac{d}{d x} (x lo g_{10} (\frac{2}{x}))

Wende die Produktregel an:

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

f = x, g = lo g_{10} (\frac{2}{x})

= \frac{d x}{d x} lo g_{10} (\frac{2}{x}) + \frac{d}{d x} (lo g_{10} (\frac{2}{x})) x

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

\frac{d}{d x} (lo g_{10} (\frac{2}{x})) = - \frac{1}{ln ( 10 ) x}

= 1 \cdot lo g_{10} (\frac{2}{x}) + (- \frac{1}{ln ( 10 ) x}) x

Vereinfache

1 \cdot lo g_{10} (\frac{2}{x}) + (- \frac{1}{ln ( 10 ) x}) x : lo g_{10} (\frac{2}{x}) - \frac{1}{ln ( 10 )}

= lo g_{10} (\frac{2}{x}) - \frac{1}{ln ( 10 )}

\int \frac{x ^{2} - 1}{x} d x

\int \frac{- x + 1}{x ^{2} + 1} d x

ma c l a u r in (\frac{1}{3})^{x}

\int_{0}^{1} 2 x + 1 d x

x \to \infty + lim (25 x^{4} + 9 x - 5 x^{2})