derivative of 3arccos(x/2)

Lösung

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

- \frac{3}{4 - x ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Vereinfache

3 - \frac{1}{1 - ( \frac{x}{2} ) ^{2}} \cdot \frac{1}{2} : - \frac{3}{4 - x ^{2}}

= - \frac{3}{4 - x ^{2}}

\int \frac{42 w ^{7} - 7 w}{7 w ^{5}} d w

s l o p e in t erce pt (4, 0), (- 2, 4)

y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{- t}, y (0) = 0, y^{^{'}} (0) = 2

\frac{d}{d x} (\frac{1}{sin ( x )})

d er i v a t i v e f (x) = ln (5)