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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

= \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

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

Vereinfache

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

Beliebte Beispiele

fläche x=y^2-1,x=y

a re a x = y^{2} - 1, x = y

derivative of 2x+x^2

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

(sin (t))^{^{'}}

derivative f(x)=4x^2-15

d er i v a t i v e f (x) = 4 x^{2} - 15

(\partial)/(\partial x)((-x^2)/(y^2))

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