derivative 3arccos(x/2)

Lösung

ableitung von

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{( x - 2 ) ( x + 3 )}{x ^{2}} d x

\frac{d}{d x} (72 cos (x))

e x t re m e f (w) = \frac{w}{w + \frac{d}{w}}

\int \frac{x}{3 x + 2} d x

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 2 y^{3})