derivative of arcsin(xy)

Lösung

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

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

Schritte zur Lösung

\frac{d}{d x} (arcsin (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}}

f (x) = \frac{x e ^{x}}{x + e ^{x}}

\int \frac{4}{( x + 2 ) ( x - 2 )} d x

\int_{0}^{1} \frac{x - 1}{x ^{2} + 3 x + 2} d x

t an g e n t f (x) = \frac{e ^{x}}{x}, at x = 1

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})