derivative of ln((x^2-81/k))

Lösung

\frac{d}{d x} (ln (\frac{x ^{2} - 81}{k}))

\frac{2 x}{x ^{2} - 81}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x ^{2} - 81}{k}))

Wende die Kettenregel an:

\frac{1}{\frac{x ^{2} - 81}{k}} \frac{d}{d x} (\frac{x ^{2} - 81}{k})

= \frac{1}{\frac{x ^{2} - 81}{k}} \frac{d}{d x} (\frac{x ^{2} - 81}{k})

\frac{d}{d x} (\frac{x ^{2} - 81}{k}) = \frac{2 x}{k}

= \frac{1}{\frac{x ^{2} - 81}{k}} \cdot \frac{2 x}{k}

Vereinfache

\frac{1}{\frac{x ^{2} - 81}{k}} \cdot \frac{2 x}{k} : \frac{2 x}{x ^{2} - 81}

= \frac{2 x}{x ^{2} - 81}

d er i v a t i v e 6 - 7 x

\frac{d}{d x} (sin^{12} (3 x^{4} - x))

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

l a pl a ce t r an s f or m 3 t^{2} - 9 t

d er i v a t i v e (4 x + 5)^{\frac{1}{5}}