derivative of ln(1+4/x)

Lösung

\frac{d}{d x} (ln (1 + \frac{4}{x}))

- \frac{4}{x ( x + 4 )}

Schritte zur Lösung

\frac{d}{d x} (ln (1 + \frac{4}{x}))

Wende die Kettenregel an:

\frac{1}{1 + \frac{4}{x}} \frac{d}{d x} (1 + \frac{4}{x})

= \frac{1}{1 + \frac{4}{x}} \frac{d}{d x} (1 + \frac{4}{x})

\frac{d}{d x} (1 + \frac{4}{x}) = - \frac{4}{x ^{2}}

= \frac{1}{1 + \frac{4}{x}} (- \frac{4}{x ^{2}})

Vereinfache

\frac{1}{1 + \frac{4}{x}} (- \frac{4}{x ^{2}}) : - \frac{4}{x ( x + 4 )}

= - \frac{4}{x ( x + 4 )}

y^{^{'}} = (y^{2} - 1) x

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 9 x})

\frac{\partial}{\partial u} (u \cdot sin (v))

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\frac{d}{d x} (x e^{- 6 x})