(\partial)/(\partial x)(-2e^{4y-x^2-y^2}x)

Lösung

\frac{\partial}{\partial x} (- 2 e^{4 y - x^{2} - y^{2}} x)

- 2 (- 2 e^{4 y - x^{2} - y^{2}} x^{2} + e^{4 y - x^{2} - y^{2}})

Schritte zur Lösung

\frac{\partial}{\partial x} (- 2 e^{4 y - x^{2} - y^{2}} x)

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \frac{\partial}{\partial x} (e^{4 y - x^{2} - y^{2}} x)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{4 y - x^{2} - y^{2}}, g = x

= - 2 (\frac{\partial}{\partial x} (e^{4 y - x^{2} - y^{2}}) x + \frac{\partial}{\partial x} (x) e^{4 y - x^{2} - y^{2}})

\frac{\partial}{\partial x} (e^{4 y - x^{2} - y^{2}}) = - 2 e^{4 y - x^{2} - y^{2}} x

\frac{\partial}{\partial x} (x) = 1

= - 2 ((- 2 e^{4 y - x^{2} - y^{2}} x) x + 1 \cdot e^{4 y - x^{2} - y^{2}})

Vereinfache

- 2 ((- 2 e^{4 y - x^{2} - y^{2}} x) x + 1 \cdot e^{4 y - x^{2} - y^{2}}) : - 2 (- 2 e^{4 y - x^{2} - y^{2}} x^{2} + e^{4 y - x^{2} - y^{2}})

= - 2 (- 2 e^{4 y - x^{2} - y^{2}} x^{2} + e^{4 y - x^{2} - y^{2}})

x \to \infty lim (x - 6)

a re a (8 cos (π x)), (8 x^{2} - 2), [- 0.5, 0.5]

\frac{\partial}{\partial y} ((x - 4) ln (x y))

\int_{0}^{l n (4)} \frac{e ^{x}}{e ^{2 x} + 25} d x

x \to - \infty lim (\frac{1}{x} + 3)