derivative of arccos((ax/2))

Lösung

\frac{d}{d x} (arccos (\frac{a x}{2}))

- \frac{a}{4 - a ^{2} x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arccos (\frac{a x}{2}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{a x}{2}) = \frac{a}{2}

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

Vereinfache

- \frac{1}{1 - ( \frac{a x}{2} ) ^{2}} \cdot \frac{a}{2} : - \frac{a}{4 - a ^{2} x ^{2}}

= - \frac{a}{4 - a ^{2} x ^{2}}

\int \frac{1}{x} - \frac{4}{x ^{2} + 1} d x

\int_{0}^{\infty} cos^{2} (x) d x

\int \frac{1}{64 e ^{- 8 x} + e ^{8 x}} d x

s l o p e (5, 7), (- 4, - 2)

\int (e^{4 x} + e^{- 4 x})^{2} d x