derivative arccos(ax)

Lösung

ableitung von

arccos (a x)

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

Schritte zur Lösung

\frac{d}{d x} (arccos (a x))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (a x) = a

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

Vereinfache

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

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