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Beliebt Rechnen >

(\partial)/(\partial y)(3xye^{-x^2-y^2})

Lösung

\frac{\partial}{\partial y} (3 x y e^{- x^{2} - y^{2}})

Lösung

3 x (e^{- x^{2} - y^{2}} - 2 e^{- x^{2} - y^{2}} y^{2})

Schritte zur Lösung

\frac{\partial}{\partial y} (3 x y e^{- x^{2} - y^{2}})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 3 x \frac{\partial}{\partial y} (y e^{- x^{2} - y^{2}})

Wende die Produktregel an:

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

f = y, g = e^{- x^{2} - y^{2}}

= 3 x (\frac{\partial}{\partial y} (y) e^{- x^{2} - y^{2}} + \frac{\partial}{\partial y} (e^{- x^{2} - y^{2}}) y)

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

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

= 3 x (1 \cdot e^{- x^{2} - y^{2}} + (- 2 e^{- x^{2} - y^{2}} y) y)

Vereinfache

3 x (1 \cdot e^{- x^{2} - y^{2}} + (- 2 e^{- x^{2} - y^{2}} y) y) : 3 x (e^{- x^{2} - y^{2}} - 2 e^{- x^{2} - y^{2}} y^{2})

= 3 x (e^{- x^{2} - y^{2}} - 2 e^{- x^{2} - y^{2}} y^{2})

Beliebte Beispiele

integral of sin(5x)sin(2x)

\int sin (5 x) sin (2 x) d x

(\partial)/(\partial x)(7xy^2)

\frac{\partial}{\partial x} (7 x y^{2})

limit as x approaches-3 of sqrt(-4x+6)

x \to - 3 lim (- 4 x + 6)

integral of cot^4(3x)

\int cot^{4} (3 x) d x

derivative (x^3)/(10(x-2))

d er i v a t i v e \frac{x ^{3}}{10 ( x - 2 )}