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Beliebt Rechnen >

(\partial)/(\partial y)(sin^2(xy))

Lösung

\frac{\partial}{\partial y} (sin^{2} (x y))

Lösung

x sin (2 x y)

Schritte zur Lösung

\frac{\partial}{\partial y} (sin^{2} (x y))

Behandle

x

als Konstante

Wende die Kettenregel an:

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

= 2 sin (x y) \frac{\partial}{\partial y} (sin (x y))

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

= 2 sin (x y) cos (x y) x

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= x sin (2 x y)

Beliebte Beispiele

y^'+(4y)/x =-3/x ,y(1)=-2

y^{^{'}} + \frac{4 y}{x} = - \frac{3}{x}, y (1) = - 2

limit as x approaches 2 of x^2+3x

x \to 2 lim (x^{2} + 3 x)

integral of 9x^{-2}

\int 9 x^{- 2} d x

derivative of (x-2/(x+2))

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

derivative y=xe^{ax}

d er i v a t i v e y = x e^{a x}