derivative f(x)=(arccos(x))^3

Lösung

ableitung von

f (x) = (arccos (x))^{3}

- \frac{3 arccos ^{2} ( x )}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((arccos (x))^{3})

Wende die Kettenregel an:

3 (arccos (x))^{2} \frac{d}{d x} (arccos (x))

= 3 (arccos (x))^{2} \frac{d}{d x} (arccos (x))

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

= 3 (arccos (x))^{2} (- \frac{1}{1 - x ^{2}})

Vereinfache

3 arccos^{2} (x) (- \frac{1}{1 - x ^{2}}) : - \frac{3 arccos ^{2} ( x )}{1 - x ^{2}}

= - \frac{3 arccos ^{2} ( x )}{1 - x ^{2}}

\int cos (3 x + 2) d x

t an g e n t f (x) = 4 (x - \frac{1}{x})^{3}, at x = 2

t an g e n t y = \frac{- 2 x}{x ^{2} + 1}, (0, 0)

x \to 0 lim (\frac{x}{csc ^{2} ( x )})

x \to 5 lim (x^{2} - 2 x + 1)