derivative of ln(x+1/x)

Lösung

\frac{d}{d x} (ln (x + \frac{1}{x}))

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

Schritte zur Lösung

\frac{d}{d x} (ln (x + \frac{1}{x}))

Wende die Kettenregel an:

\frac{1}{x + \frac{1}{x}} \frac{d}{d x} (x + \frac{1}{x})

= \frac{1}{x + \frac{1}{x}} \frac{d}{d x} (x + \frac{1}{x})

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

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

Vereinfache

\frac{1}{x + \frac{1}{x}} (1 - \frac{1}{x ^{2}}) : \frac{x ^{2} - 1}{x ( x ^{2} + 1 )}

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

\int_{0}^{1} x^{8} d x

\int \frac{7}{x ^{2}} cos (\frac{7}{x}) d x

h \to 0 lim (x^{2} + 2 x + h - 69)

y^{^{'}} (t) = (3 + y) (1 - y), y (0) = 2

y^{^{'}} + 2 y = \frac{1}{x}