(\partial)/(\partial x)((u(x,y))(x+y))

Lösung

\frac{\partial}{\partial x} ((u (x, y)) (x + y))

u ((, y \cdot 1) (x + y) + 1 \cdot (x, y))

Schritte zur Lösung

\frac{\partial}{\partial x} ((u (x, y)) (x + y))

Behandle

u, y

als Konstanten

Entferne die Konstante:

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

= u \frac{\partial}{\partial x} ((x, y) (x + y))

Wende die Produktregel an:

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

f = x, y, g = x + y

= u (\frac{\partial}{\partial x} (x, y) (x + y) + \frac{\partial}{\partial x} (x + y) (x, y))

\frac{\partial}{\partial x} (x, y) = (, y \cdot 1)

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

= u ((, y \cdot 1) (x + y) + 1 \cdot (x, y))

e x p an d (1 - x^{\frac{1}{2}})^{3}

e x p an d (1 - tan^{2} (x)) (1 - tan^{2} (2 x)) tan (4 x)

e x p an d (x^{\frac{1}{3}} - \frac{1}{4} x^{- \frac{1}{3}})^{2}

e x p an d tan (h) (x - y)

e x p an d (x + ln (x))^{2}