derivative of arccos(9/x)

Lösung

\frac{d}{d x} (arccos (\frac{9}{x}))

\frac{9}{x x ^{2} - 81}

Schritte zur Lösung

\frac{d}{d x} (arccos (\frac{9}{x}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{1 - ( \frac{9}{x} ) ^{2}} (- \frac{9}{x ^{2}}) : \frac{9}{x x ^{2} - 81}

= \frac{9}{x x ^{2} - 81}

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

\frac{d ^{2}}{d x ^{2}} (e^{\frac{4}{x}})

\int \frac{3 x}{x ^{2} + 2 x + 5} d x

\int \frac{( 2 x - 3 )}{9 - x ^{2}} d x

y^{^{'}} = - 0.5 y^{1.5}