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Beliebt Rechnen >

(\partial)/(\partial y)(xye^{(xy)})

Lösung

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

Lösung

x (e^{x y} + e^{x y} x y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{x y}

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

\frac{\partial}{\partial y} (y) = 1

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

= x (1 \cdot e^{x y} + e^{x y} x y)

Vereinfache

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

Beliebte Beispiele

derivative f(x)=3x^2-4x+1

d er i v a t i v e f (x) = 3 x^{2} - 4 x + 1

derivative of sin(xsec(x))

\frac{d}{d x} (sin (x) sec (x))

integral from-2 to 2 of 2

\int_{- 2}^{2} 2 d x

derivative y=3x^2sin(x)

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

2y^{''}+3y^'-2y=25e^{-2t}

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 25 e^{- 2 t}