derivative of arccos((x+1/3))

Lösung

\frac{d}{d x} (arccos (\frac{x + 1}{3}))

- \frac{1}{- x ^{2} - 2 x + 8}

Schritte zur Lösung

\frac{d}{d x} (arccos (\frac{x + 1}{3}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x + 1}{3}) = \frac{1}{3}

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

Vereinfache

- \frac{1}{1 - ( \frac{x + 1}{3} ) ^{2}} \cdot \frac{1}{3} : - \frac{1}{- x ^{2} - 2 x + 8}

= - \frac{1}{- x ^{2} - 2 x + 8}

y^{^{'}} = x + y, y (0) = 0

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

\frac{\partial}{\partial y} (x^{\frac{3}{4}} y^{\frac{1}{4}})

a re a y = x^{2}, y = 4

d er i v a t i v e f (t) = e^{5 t s i n (2 t)}