(\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})})

Vereinfache

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

= \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

x \to 8 lim (x - 2)

x \to 2 lim (\frac{7}{( x - 2 ) ^{2}})

cos (x) y^{^{'}} + sin (x) y = 2 cos^{3} (x) sin (x) - 1

x \to \infty lim (3)

d er i v a t i v e f (x) = tan^{2} (sin (θ))