derivative of (f(x(6x))^2-4)

Lösung

\frac{d}{d x} ((f (x) (6 x))^{2} - 4)

36 (2 x^{2} f (x) \frac{d}{d x} (f (x)) + 2 x f (x)^{2})

Schritte zur Lösung

\frac{d}{d x} ((f (x) (6 x))^{2} - 4)

Vereinfache

(f (x) (6 x))^{2} - 4 : 36 x^{2} f (x)^{2} - 4

= \frac{d}{d x} (36 x^{2} f (x)^{2} - 4)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (36 x^{2} f (x)^{2}) - \frac{d}{d x} (4)

\frac{d}{d x} (36 x^{2} f (x)^{2}) = 36 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2})

\frac{d}{d x} (4) = 0

= 36 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}) - 0

Vereinfache

= 36 (2 x^{2} f (x) \frac{d}{d x} (f (x)) + 2 x f (x)^{2})

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