(\partial)/(\partial t)((u(t,x))(3x-2t))

Lösung

\frac{\partial}{\partial t} ((u (t, x)) (3 x - 2 t))

u ((, x \cdot 1) (3 x - 2 t) + (- 2) (t, x))

Schritte zur Lösung

\frac{\partial}{\partial t} ((u (t, x)) (3 x - 2 t))

Behandle

u, x

als Konstanten

Entferne die Konstante:

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

= u \frac{\partial}{\partial t} ((t, x) (3 x - 2 t))

Wende die Produktregel an:

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

f = t, x, g = 3 x - 2 t

= u (\frac{\partial}{\partial t} (t, x) (3 x - 2 t) + \frac{\partial}{\partial t} (3 x - 2 t) (t, x))

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

\frac{\partial}{\partial t} (3 x - 2 t) = - 2

= u ((, x \cdot 1) (3 x - 2 t) + (- 2) (t, x))

e x p an d - \frac{d}{d s} (\frac{a}{s ( s ^{2} - b )})

e x p an d - \frac{12 ( 6 + 2 )}{17}

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

e x p an d \frac{( k ^{2} + 2 k + 1 ) ( k ^{2} + 4 k + 4 )}{4}

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