derivative of x^2+{z}(x(x)^2)

Lösung

\frac{d}{d x} (x^{2} + z (x) (x)^{2})

2 x + \frac{d}{d x} (z (x)) x^{2} + 2 x z (x)

Schritte zur Lösung

\frac{d}{d x} (x^{2} + z (x) (x)^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (z (x) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (z (x) x^{2}) = \frac{d}{d x} (z (x)) x^{2} + 2 x z (x)

= 2 x + \frac{d}{d x} (z (x)) x^{2} + 2 x z (x)