derivative of arcsin(x-y)

Lösung

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

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

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

Vereinfache

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

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

\int_{- 1}^{3} 3 x + 1 d x

t an g e n t y = x^{2}, at x = \frac{1}{3}

\frac{\partial}{\partial y} (\frac{5 ( y + 2 )}{( x + 2 ) ^{2}})

\frac{\partial}{\partial x} (y^{x} - ln (x^{4} y + 6 x))

\frac{\partial}{\partial y} (2 x^{2} - 3 y^{2} - 2 x)