(\partial}{\partial x}(e^{-\frac{x^2)/6-(y^2)/6})

Lösung

\frac{\partial}{\partial x} (e^{- \frac{x ^{2}}{6} - \frac{y ^{2}}{6}})

- \frac{e ^{\frac{- x ^{2} - y ^{2}}{6}} x}{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{- \frac{x ^{2}}{6} - \frac{y ^{2}}{6}})

Vereinfache

e^{- \frac{x ^{2}}{6} - \frac{y ^{2}}{6}} : e^{\frac{- x ^{2} - y ^{2}}{6}}

= \frac{\partial}{\partial x} (e^{\frac{- x ^{2} - y ^{2}}{6}})

Behandle

y

als Konstante

Wende die Kettenregel an:

e^{\frac{- x ^{2} - y ^{2}}{6}} \frac{\partial}{\partial x} (\frac{- x ^{2} - y ^{2}}{6})

= e^{\frac{- x ^{2} - y ^{2}}{6}} \frac{\partial}{\partial x} (\frac{- x ^{2} - y ^{2}}{6})

\frac{\partial}{\partial x} (\frac{- x ^{2} - y ^{2}}{6}) = - \frac{x}{3}

= e^{\frac{- x ^{2} - y ^{2}}{6}} (- \frac{x}{3})

Vereinfache

e^{\frac{- x ^{2} - y ^{2}}{6}} (- \frac{x}{3}) : - \frac{e ^{\frac{- x ^{2} - y ^{2}}{6}} x}{3}

= - \frac{e ^{\frac{- x ^{2} - y ^{2}}{6}} x}{3}

n = 1 \sum \infty (cos (1.6))^{n}

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

x \to 0 - lim (\frac{∣ 8 x ∣}{x})

\frac{d}{d x} (x \cdot e^{- b x^{2}})

d er i v a t i v e 7 e^{x}