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Beliebt Rechnen >

(\partial)/(\partial x)(3xe^{xy})

Lösung

\frac{\partial}{\partial x} (3 x e^{x y})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x e^{x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} (x e^{x y})

Wende die Produktregel an:

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

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

= 3 (\frac{\partial}{\partial x} (x) e^{x y} + \frac{\partial}{\partial x} (e^{x y}) x)

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

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

= 3 (1 \cdot e^{x y} + e^{x y} y x)

Vereinfache

= 3 (e^{x y} + e^{x y} x y)

Beliebte Beispiele

derivative xsin(y)

d er i v a t i v e x sin (y)

limit as x approaches-infinity of-2x-1

x \to - \infty lim (- 2 x - 1)

integral of sqrt(25-4x^2)

\int 25 - 4 x^{2} d x

tangent y=2sin(x),\at x= pi/4

t an g e n t y = 2 sin (x), at x = \frac{π}{4}

integral of sec^3(x)tan^2(x)

\int sec^{3} (x) tan^{2} (x) d x