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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = e^{8 x y}

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

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

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

= 2 (1 \cdot e^{8 x y} + e^{8 x y} \cdot 8 y x)

Vereinfache

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

d er i v a t i v e y = 7 e^{x} + \frac{4}{3 x}

x \to 0 lim (\frac{9 ^{x} - 1 0 ^{x}}{x})

\int 4 3 x d x

z \to (1 - i) lim (x + i (2 x + y))

t an g e n t \frac{x}{x ^{2} + 16}