(\partial)/(\partial u)((x)(u^2-v^2))

Lösung

\frac{\partial}{\partial u} ((x) (u^{2} - v^{2}))

2 xu

Schritte zur Lösung

\frac{\partial}{\partial u} ((x) (u^{2} - v^{2}))

Behandle

x, v

als Konstanten

Entferne die Konstante:

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

= x \frac{\partial}{\partial u} (u^{2} - v^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{\partial}{\partial u} (u^{2}) - \frac{\partial}{\partial u} (v^{2}))

\frac{\partial}{\partial u} (u^{2}) = 2 u

\frac{\partial}{\partial u} (v^{2}) = 0

= x (2 u - 0)

Vereinfache

= 2 xu

s im pl i f y (i - 2)^{4}

e x p an d (e^{x} + e^{- x})^{2} \cdot e^{2 x} \cdot (e^{x} - 1)^{2}

e x p an d (t^{2} + 1) (2 t^{2} + 1)

e x p an d \frac{s ^{2} + 6 s + 9}{( s + 4 ) ( s ^{2} - 3 s + 2 )}

e x p an d \frac{1}{( s - 5 ) ^{2}}