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Beliebt Rechnen >

(\partial)/(\partial y)((1+xy)e^{xy})

Lösung

\frac{\partial}{\partial y} ((1 + x y) e^{x y})

Lösung

2 e^{x y} x + e^{x y} x^{2} y

Schritte zur Lösung

\frac{\partial}{\partial y} ((1 + x y) e^{x y})

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = 1 + x y, g = e^{x y}

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

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

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

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

Vereinfache

x e^{x y} + e^{x y} x (1 + x y) : 2 e^{x y} x + e^{x y} x^{2} y

= 2 e^{x y} x + e^{x y} x^{2} y

Beliebte Beispiele

sum from n=1 to infinity of (9^n)/(10^n)

n = 1 \sum \infty \frac{9 ^{n}}{1 0 ^{n}}

integral of sec^3(8x)

\int sec^{3} (8 x) d x

integral of x^2sqrt(2x+5)

\int x^{2} 2 x + 5 d x

tangent y= 3/(sqrt(x)),(4, 3/2)

t an g e n t y = \frac{3}{x}, (4, \frac{3}{2})

laplacetransform t^2cos(t)

l a pl a ce t r an s f or m t^{2} cos (t)