derivative of 1/(arccos(3x))

Lösung

\frac{d}{d x} (\frac{1}{arccos ( 3 x )})

\frac{3}{arccos ^{2} ( 3 x ) 1 - 9 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{arccos ( 3 x )})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (arccos (3 x)) = - \frac{3}{1 - 9 x ^{2}}

= - \frac{1}{( arccos ( 3 x ) ) ^{2}} (- \frac{3}{1 - 9 x ^{2}})

Vereinfache

- \frac{1}{arccos ^{2} ( 3 x )} (- \frac{3}{1 - 9 x ^{2}}) : \frac{3}{arccos ^{2} ( 3 x ) 1 - 9 x ^{2}}

= \frac{3}{arccos ^{2} ( 3 x ) 1 - 9 x ^{2}}

\int x^{2} cos (y) d y

\frac{d}{d t} (2 + 4 t)

\int cos^{3} (\frac{x}{16}) d x

n = 0 \sum \infty e^{- a \cdot n}

a re a f (x) = x^{2} - 4, g (x) = 0