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Beliebt Rechnen >

(\partial)/(\partial x)(e^ysin(xy))

Lösung

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

Lösung

e^{y} cos (x y) y

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= e^{y} \frac{\partial}{\partial x} (sin (x y))

Wende die Kettenregel an:

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

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

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

= e^{y} cos (x y) y

Beliebte Beispiele

derivative of (12x^2-x^4/((4-x^2)^2))

\frac{d}{d x} (\frac{12 x ^{2} - x ^{4}}{( 4 - x ^{2} ) ^{2}})

derivative f(x)=(x-3)(2x+4)

d er i v a t i v e f (x) = (x - 3) (2 x + 4)

y^{^{'}} = - \frac{1}{40} y

derivative 7e^{-x}

d er i v a t i v e 7 e^{- x}

(dy)/(dx)+1/2 y=0

\frac{d y}{d x} + \frac{1}{2} y = 0