derivative of (3x^2+ln(x)*(5x^3)^x)

Lösung

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

(6 x + \frac{1}{x}) (5 x^{3})^{x} + (ln (5 x^{3}) + 3) (5 x^{3})^{x} (3 x^{2} + ln (x))

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x^{2} + ln (x), g = (5 x^{3})^{x}

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

\frac{d}{d x} (3 x^{2} + ln (x)) = 6 x + \frac{1}{x}

\frac{d}{d x} ((5 x^{3})^{x}) = (ln (5 x^{3}) + 3) (5 x^{3})^{x}

= (6 x + \frac{1}{x}) (5 x^{3})^{x} + (ln (5 x^{3}) + 3) (5 x^{3})^{x} (3 x^{2} + ln (x))

\int 7 sin^{5} (x) cos (x) d x

x \to \infty lim (\frac{3 x - 2}{6 x + 1})

d er i v a t i v e f (x) = arccot (e^{x})

d er i v a t i v e y = x^{2} + x^{- 2} + 7 x - 1

\int x^{3} e^{3 x^{4}} d x