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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Beliebte Beispiele

(2xy-3)dx+(x^2+4y)dy=0,y(1)=2

(2 x y - 3) d x + (x^{2} + 4 y) d y = 0, y (1) = 2

integral of 2x^2sqrt(x^3+1)

\int 2 x^{2} x^{3} + 1 d x

limit as x approaches+2 of (2x-25)/(x-2)

x \to + 2 lim (\frac{2 x - 25}{x - 2})

f(t)=arcsin(1/t)

f (t) = arcsin (\frac{1}{t})

limit as x approaches-0.1 of (sin(3x))/x

x \to - 0.1 lim (\frac{sin ( 3 x )}{x})