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Beliebt Rechnen >

(\partial)/(\partial x)(2xe^{4xy})

Lösung

\frac{\partial}{\partial x} (2 x e^{4 x y})

Lösung

2 (e^{4 x y} + 4 e^{4 x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x e^{4 x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial x} (x e^{4 x y})

Wende die Produktregel an:

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

f = x, g = e^{4 x y}

= 2 (\frac{\partial}{\partial x} (x) e^{4 x y} + \frac{\partial}{\partial x} (e^{4 x y}) x)

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

\frac{\partial}{\partial x} (e^{4 x y}) = e^{4 x y} \cdot 4 y

= 2 (1 \cdot e^{4 x y} + e^{4 x y} \cdot 4 y x)

Vereinfache

= 2 (e^{4 x y} + 4 e^{4 x y} x y)

Beliebte Beispiele

integral of x^3(4-x^2)^{1/4}

\int x^{3} (4 - x^{2})^{\frac{1}{4}} d x

integral from 0 to 1 of x^2(x+1)^6

\int_{0}^{1} x^{2} (x + 1)^{6} d x

inverselaplace 6/(s(s+3))

in v erse l a pl a ce \frac{6}{s ( s + 3 )}

derivative of asin^3(x)

\frac{d}{d x} (a sin^{3} (x))

limit as x approaches 0-of (14x^3+15x)/x

x \to 0 - lim (\frac{14 x ^{3} + 15 x}{x})