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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

d er i v a t i v e x = 4 t^{2} - 3 t + 11

\frac{d}{d x} (sin^{2} (x) + sin (x))

a re a x = 4 y^{2}, x = 2 + 2 y^{2}

\frac{\partial}{\partial x} (4 x^{2} + x y + 3 y^{2} - 8)

t an g e n t f (x) = 2 x^{2}, at x = 5