(\partial)/(\partial x)(8xe^{x^2}+y^2)

Lösung

\frac{\partial}{\partial x} (8 x e^{x^{2}} + y^{2})

8 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Schritte zur Lösung

\frac{\partial}{\partial x} (8 x e^{x^{2}} + y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (8 x e^{x^{2}}) + \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (8 x e^{x^{2}}) = 8 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

\frac{\partial}{\partial x} (y^{2}) = 0

= 8 (e^{x^{2}} + 2 e^{x^{2}} x^{2}) + 0

Vereinfache

= 8 (2 e^{x^{2}} x^{2} + e^{x^{2}})

x \to \infty lim (3 \frac{5 - 8 x}{x + 3})

\int \frac{x + 4}{x ^{2} + 4} d x

a re a (x + 2)^{3}, 2 x^{2} - 8 x + 8, 0

x \to 1 lim (x + 4 - 12)

t an g e n t f (x) = x + 2, at x = 1