derivative of (f(x(3x))^2+5)

Lösung

\frac{d}{d x} ((f (x) (3 x))^{2} + 5)

9 (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) (3 x))^{2} + 5)

Vereinfache

(f (x) (3 x))^{2} + 5 : 9 x^{2} f (x)^{2} + 5

= \frac{d}{d x} (9 x^{2} f (x)^{2} + 5)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (9 x^{2} f (x)^{2}) + \frac{d}{d x} (5)

\frac{d}{d x} (9 x^{2} f (x)^{2}) = 9 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2})

\frac{d}{d x} (5) = 0

= 9 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}) + 0

Vereinfache

= 9 (2 x^{2} f (x) \frac{d}{d x} (f (x)) + 2 x f (x)^{2})

x \to 2 lim (5 x^{2} - 3 x + 1)

\frac{d}{d x} (ln (x 4 x - 1))

x \to + 0 lim (\frac{sin ^{2} ( x )}{x})

\int_{3}^{5} e^{x} d x

a re a y = - 2 x, y = 2 x, x = 0, x = 16