derivative of arccos(sqrt(y-2x))

Lösung

\frac{d}{d x} (arccos (y - 2 x))

- \frac{\frac{d y}{d x} - 2}{2 1 - y + 2 x y - 2 x}

Schritte zur Lösung

\frac{d}{d x} (arccos (y - 2 x))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (y - 2 x) = \frac{\frac{d y}{d x} - 2}{2 y - 2 x}

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

Vereinfache

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

= - \frac{\frac{d y}{d x} - 2}{2 1 - y + 2 x y - 2 x}

\int sec^{2} (θ) tan^{7} (θ) d θ

x \to 2 lim (\frac{- 1}{( x + 2 )})

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

x \to 0 lim (16 - 7 x)

\int - cos (x) + C d x