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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

y^{^{''}} - y^{^{'}} - 2 y = 8 e - t

f (x) = x^{\frac{1}{x}}

\frac{\partial}{\partial y} (y + y cos (x y))

d er i v a t i v e \frac{1}{2 x + 25}

\int \frac{19}{x 1 + 2 x} d x