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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

d er i v a t i v e \frac{1}{x ^{2} + 4}

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

t an g e n t f (x) = \frac{4 x}{x + 3}, (1, 1)

\frac{d}{d θ} (cos (θ) - θ sin (θ))