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Beliebt Rechnen >

(\partial)/(\partial y)(-xsin(xy))

Lösung

\frac{\partial}{\partial y} (- x sin (x y))

Lösung

- x^{2} cos (x y)

Schritte zur Lösung

\frac{\partial}{\partial y} (- x sin (x y))

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= - x cos (x y) x

Vereinfache

- x cos (x y) x : - x^{2} cos (x y)

= - x^{2} cos (x y)

Beliebte Beispiele

integral of e^{t/2}cos(2t)

\int e^{\frac{t}{2}} cos (2 t) d t

integral of cos^3(x)ln(sin(x))

\int cos^{3} (x) ln (sin (x)) d x

derivative f(x)=(3x+2)/(3x-2)

d er i v a t i v e f (x) = \frac{3 x + 2}{3 x - 2}

derivative of sqrt(3x+2y)

\frac{d}{d x} (3 x + 2 y)

derivative of sqrt(25+x^2)

\frac{d}{d x} (25 + x^{2})