(\partial)/(\partial x)(e^{-2x^2-3y^2})

Lösung

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

- 4 e^{- 2 x^{2} - 3 y^{2}} x

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= e^{- 2 x^{2} - 3 y^{2}} (- 4 x)

Vereinfache

= - 4 e^{- 2 x^{2} - 3 y^{2}} x

\int 9 x^{3} (x^{3} + 2 x^{2} + x + 8) d x

x \to 4 - lim (c x^{2} + 7 x)

\int \frac{1}{2} (x - \frac{1}{2} sin (2 x)) d x

d er i v a t i v e f (x) = \frac{2}{3 x ^{2}}

\frac{d}{d x} (\frac{4 3 x ^{2}}{x ^{2} - 8 x})