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Beliebt Rechnen >

(\partial)/(\partial x)(e^{xy}x)

Lösung

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

Lösung

e^{x y} x y + e^{x y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

Beliebte Beispiele

derivative of sin(x+pi/2)

\frac{d}{d x} (sin (x + \frac{π}{2}))

integral of (x^6-3x^2)^4(x^5-x)

\int (x^{6} - 3 x^{2})^{4} (x^{5} - x) d x

\frac{d}{d t} (3 - 3 t)

(\partial)/(\partial x)(cos(x)y)

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

fläche 5x,x^2-6

a re a 5 x, x^{2} - 6