(\partial)/(\partial x)(9xe^{4xy})

Lösung

\frac{\partial}{\partial x} (9 x e^{4 x y})

9 (e^{4 x y} + 4 e^{4 x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (9 x e^{4 x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 9 \frac{\partial}{\partial x} (x e^{4 x y})

Wende die Produktregel an:

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

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

= 9 (\frac{\partial}{\partial x} (x) e^{4 x y} + \frac{\partial}{\partial x} (e^{4 x y}) x)

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

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

= 9 (1 \cdot e^{4 x y} + e^{4 x y} \cdot 4 y x)

Vereinfache

= 9 (e^{4 x y} + 4 e^{4 x y} x y)

\frac{\partial}{\partial x} (\frac{x + y}{2})

in v erse l a pl a ce \frac{3}{( s + 1 ) ^{2}}

n = 1 \sum \infty \frac{4 ^{n}}{2 ^{n}}

s l o p e x y - 3 y^{2} = 8, (14, 4)

\int x e^{- x} d x