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Beliebt Rechnen >

(\partial)/(\partial x)(17xye^{-x^2-y^2})

Lösung

\frac{\partial}{\partial x} (17 x y e^{- x^{2} - y^{2}})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (17 x y e^{- x^{2} - y^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 17 y \frac{\partial}{\partial x} (x e^{- x^{2} - y^{2}})

Wende die Produktregel an:

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

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

= 17 y (\frac{\partial}{\partial x} (x) e^{- x^{2} - y^{2}} + \frac{\partial}{\partial x} (e^{- x^{2} - y^{2}}) x)

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

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

= 17 y (1 \cdot e^{- x^{2} - y^{2}} + (- 2 e^{- x^{2} - y^{2}} x) x)

Vereinfache

17 y (1 \cdot e^{- x^{2} - y^{2}} + (- 2 e^{- x^{2} - y^{2}} x) x) : 17 y (e^{- x^{2} - y^{2}} - 2 e^{- x^{2} - y^{2}} x^{2})

= 17 y (e^{- x^{2} - y^{2}} - 2 e^{- x^{2} - y^{2}} x^{2})

Beliebte Beispiele

sum from n=1 to infinity of n/(3n^3+1)

n = 1 \sum \infty \frac{n}{3 n ^{3} + 1}

limit as x approaches-1+of (3x-5)/(x+1)

x \to - 1 + lim (\frac{3 x - 5}{x + 1})

solvefor x,(d^2y)/(dx^2)=y^2

so l v e f or x, \frac{d ^{2} y}{d x ^{2}} = y^{2}

(arctan(cos(x)))^'

(arctan (cos (x)))^{^{'}}

y^{''}-y^'-6y=20e^{-2x}

y^{^{''}} - y^{^{'}} - 6 y = 20 e^{- 2 x}