d/(d{x)}(e^{-({x}^2+{y}^2+{z}^2)})

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

\frac{d y}{d x} = \frac{( x ^{3} + y ^{3} )}{3 \cdot x \cdot y ^{2}}

\frac{d y}{d x} = \frac{y ^{2}}{x ^{3}}

\int 7 x^{2} 1 - x^{3} d x

\frac{d y}{e ^{5 y}} = e^{4 x} d x

x \to \infty lim (- x^{4})