(\partial)/(\partial x)(x(x+y)2)

Lösung

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

2 (2 x + y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = x + y

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

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

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

= 2 (1 \cdot (x + y) + 1 \cdot x)

Vereinfache

2 (1 \cdot (x + y) + 1 \cdot x) : 2 (2 x + y)

= 2 (2 x + y)

\int e^{x} \cdot cos (x) d x

x \to 0 + lim (x^{2} + 5)

\int_{0}^{\frac{π}{6}} 8 sec^{3} (x) d x

a re a \frac{2}{x}, 8 x, \frac{x}{8}

x \to 5 lim (\frac{20 - 4 x}{x - 5})