derivative of e^{aarccos(x})

Lösung

\frac{d}{d x} (e^{a a r c c o s (x)})

- \frac{a e ^{a a r c c o s (x)}}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (e^{a a r c c o s (x)})

Wende die Kettenregel an:

e^{a a r c c o s (x)} \frac{d}{d x} (a arccos (x))

= e^{a a r c c o s (x)} \frac{d}{d x} (a arccos (x))

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

= e^{a a r c c o s (x)} (- \frac{a}{1 - x ^{2}})

Vereinfache

e^{a a r c c o s (x)} (- \frac{a}{1 - x ^{2}}) : - \frac{a e ^{a a r c c o s (x)}}{1 - x ^{2}}

= - \frac{a e ^{a a r c c o s (x)}}{1 - x ^{2}}

a re a 2 cos (9 x), 2 - 2 cos (9 x), [0, \frac{π}{9}]

\int 6 arctan (x) d x

x \to 8 + lim (\frac{1}{∣ 8 - x ∣})

t a y l or sin (8 x)

\frac{d y}{d x} = b - a y