derivative of ln((7x^2+x/(x^2)))

Lösung

\frac{d}{d x} (ln (\frac{7 x ^{2} + x}{x ^{2}}))

- \frac{1}{x ( 7 x + 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{7 x ^{2} + x}{x ^{2}}))

Vereinfache

ln (\frac{7 x ^{2} + x}{x ^{2}}) : ln (\frac{7 x + 1}{x})

= \frac{d}{d x} (ln (\frac{7 x + 1}{x}))

Wende die Kettenregel an:

\frac{1}{\frac{7 x + 1}{x}} \frac{d}{d x} (\frac{7 x + 1}{x})

= \frac{1}{\frac{7 x + 1}{x}} \frac{d}{d x} (\frac{7 x + 1}{x})

\frac{d}{d x} (\frac{7 x + 1}{x}) = - \frac{1}{x ^{2}}

= \frac{1}{\frac{7 x + 1}{x}} (- \frac{1}{x ^{2}})

Vereinfache

\frac{1}{\frac{7 x + 1}{x}} (- \frac{1}{x ^{2}}) : - \frac{1}{x ( 7 x + 1 )}

= - \frac{1}{x ( 7 x + 1 )}

d er i v a t i v e y = (\frac{x}{5 + x})

\frac{d}{d x} (e^{- 2 x} sin (2 x))

\int_{0}^{1} \frac{1}{x ^{1.5}} d x

\int 7 x^{2} e^{2 x} d x

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y - 5 y^{3})