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

Lösung

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

e^{- x^{2} + 2 xv t - v^{2} t^{2}} (- 2 x + 2 v t)

Schritte zur Lösung

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

Vereinfache

e^{- (x - v t)^{2}} : e^{- x^{2} + 2 xv t - v^{2} t^{2}}

= \frac{\partial}{\partial x} (e^{- x^{2} + 2 xv t - v^{2} t^{2}})

Behandle

v, t

als Konstanten

Wende die Kettenregel an:

e^{- x^{2} + 2 xv t - v^{2} t^{2}} \frac{\partial}{\partial x} (- x^{2} + 2 xv t - v^{2} t^{2})

= e^{- x^{2} + 2 xv t - v^{2} t^{2}} \frac{\partial}{\partial x} (- x^{2} + 2 xv t - v^{2} t^{2})

\frac{\partial}{\partial x} (- x^{2} + 2 xv t - v^{2} t^{2}) = - 2 x + 2 v t

= e^{- x^{2} + 2 xv t - v^{2} t^{2}} (- 2 x + 2 v t)

\frac{\partial}{\partial x} (x cos (x) sin (x))

d er i v a t i v e f (x) = cos (x) sec (x)

d er i v a t i v e x^{2} - 5

\frac{d}{d x} ((2 x)^{3 x})

\frac{d}{d x} (5 x - 9)