derivative of arccos(((x+1)/2))

Lösung

\frac{d}{d x} (arccos (\frac{( x + 1 )}{2}))

- \frac{1}{- x ^{2} - 2 x + 3}

Schritte zur Lösung

\frac{d}{d x} (arccos (\frac{( x + 1 )}{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{1}{- x ^{2} - 2 x + 3}

\int_{- 7}^{0} \frac{1}{9 - x} d x

\frac{d}{d x} (\frac{x ^{5}}{x ^{3}})

\frac{d}{d x} (5 x^{2} cos (x) + x)

\frac{\partial}{\partial y} (\frac{( y + x )}{( y - x )})

t an g e n t f (x) = x^{2} - 2