derivative of ln(x/(sqrt(x^2+1)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (m sin (2 (m x + n y)))

\int_{2}^{e} \frac{1}{x ln ( x )} d x

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d er i v a t i v e 3 t^{2} + 5 t^{3}

\int x sin (9 x^{2}) d x