derivative of ln(x+sqrt(x^2-6))

Lösung

\frac{d}{d x} (ln (x + x^{2} - 6))

\frac{1}{x ^{2} - 6}

Schritte zur Lösung

\frac{d}{d x} (ln (x + x^{2} - 6))

Wende die Kettenregel an:

\frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

= \frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

\frac{d}{d x} (x + x^{2} - 6) = 1 + \frac{x}{x ^{2} - 6}

= \frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6})

Vereinfache

\frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6}) : \frac{1}{x ^{2} - 6}

= \frac{1}{x ^{2} - 6}

\int + \frac{40}{1 - cos ( 8 x )} d x

\frac{\partial}{\partial x} (9 - x^{2} - y^{2})

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

t an g e n t y = \frac{π}{( 2 x ) ^{4}}

\int \frac{2}{x ^{2} + 9} d x