derivative of {f}(x({g}(x)(2x)))

Lösung

\frac{d}{d x} (f (x) (g (x) (2 x)))

2 (\frac{d}{d x} (f (x)) g (x) x + (x \frac{d}{d x} (g (x)) + g (x)) f (x))

Schritte zur Lösung

\frac{d}{d x} (f (x) (g (x) (2 x)))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (f (x) g (x) x)

Wende die Produktregel an:

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

f = f (x), g = g (x) x

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

\frac{d}{d x} (g (x) x) = x \frac{d}{d x} (g (x)) + g (x)

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

\int ln (x + (x^{2} + 1)) d x

x \to 1 lim (\frac{x ^{2} - 4}{x - 2})

d er i v a t i v e 4 (5 - 9 x)^{5}

\int (\frac{6}{x} + \frac{x}{6}) d x

d er i v a t i v e (1 + cos^{2} (x))^{9}