derivative of {f}(x(x^3))

Lösung

\frac{d}{d x} (f (x) (x^{3}))

\frac{d}{d x} (f (x)) x^{3} + 3 x^{2} f (x)

Schritte zur Lösung

\frac{d}{d x} (f (x) (x^{3}))

Wende die Produktregel an:

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

f = f (x), g = x^{3}

= \frac{d}{d x} (f (x)) x^{3} + \frac{d}{d x} (x^{3}) f (x)

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{d}{d x} (f (x)) x^{3} + 3 x^{2} f (x)