derivative of arccos(xy)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Vereinfache

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

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

\frac{d}{d x} (5 (3 x^{2} + 5 x) (1 - x)^{2})

\frac{d}{d x} (\frac{3}{x ^{3}} - \frac{4}{x ^{2}})

\frac{d}{d x} (x^{5} e^{7 x})

x \to 1 lim ((x - 1)^{3 x - 3})

x \to 2 lim (x 13 - x^{2})