(\partial)/(\partial x)(arcsin(xy))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x y) = y

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

Vereinfache

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

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

d er i v a t i v e x^{2} sin^{3} (3 x)

d er i v a t i v e x^{10} arctan (x)

\frac{\partial}{\partial y} (15 - 5 (y + 3)^{2})

\frac{\partial}{\partial x} (7 x^{3} cos (7 x^{2} y))

\frac{\partial}{\partial y} (3 x^{4} y^{2} + 1)