(\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 \frac{( 100 \cdot ( s + 25 ) )}{( s \cdot ( s + 5 ) ^{3} )}

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

e x p an d (2 + j + k) (1 - 2 + 2) (3 - 4 = 2 k)

e x p an d \frac{3 x ^{2} - 7 x - 12}{( x + 4 ) ( x - 4 ) ^{2}}

e x p an d 3 sin (2 (π - θ))