(\partial)/(\partial u)((x)(u^4+vw))

Lösung

\frac{\partial}{\partial u} ((x) (u^{4} + v w))

4 x u^{3}

Schritte zur Lösung

\frac{\partial}{\partial u} ((x) (u^{4} + v w))

Behandle

x, v, w

als Konstanten

Entferne die Konstante:

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

= x \frac{\partial}{\partial u} (u^{4} + v w)

Wende die Summen-/Differenzregel an:

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

= x (\frac{\partial}{\partial u} (u^{4}) + \frac{\partial}{\partial u} (v w))

\frac{\partial}{\partial u} (u^{4}) = 4 u^{3}

\frac{\partial}{\partial u} (v w) = 0

= x (4 u^{3} + 0)

Vereinfache

= 4 x u^{3}

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

s im pl i f y 3 (1 + sin (a)) (1 - sin (a))

e x p an d (x^{2} - 5 x + 4) d x

e x p an d \frac{4 ( - n - 2 )}{n}

e x p an d (\frac{7}{3} x^{3} + 6) (\frac{7}{3} x^{3} - 6)