derivative f(x)=-3\sqrt[3]{x}*sec(2x)

Lösung

ableitung von

f (x) = - 3 3 x \cdot sec (2 x)

- \frac{sec ( 2 x )}{x ^{\frac{2}{3}}} - 6 3 x sec (2 x) tan (2 x)

Schritte zur Lösung

\frac{d}{d x} (- 3 3 x sec (2 x))

Entferne die Konstante:

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

= - 3 \frac{d}{d x} (3 x sec (2 x))

Wende die Produktregel an:

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

f = 3 x, g = sec (2 x)

= - 3 (\frac{d}{d x} (3 x) sec (2 x) + \frac{d}{d x} (sec (2 x)) 3 x)

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

\frac{d}{d x} (sec (2 x)) = sec (2 x) tan (2 x) \cdot 2

= - 3 (\frac{1}{3 x ^{\frac{2}{3}}} sec (2 x) + sec (2 x) tan (2 x) \cdot 2 3 x)

Vereinfache

- 3 (\frac{1}{3 x ^{\frac{2}{3}}} sec (2 x) + sec (2 x) tan (2 x) \cdot 2 3 x) : - \frac{sec ( 2 x )}{x ^{\frac{2}{3}}} - 6 3 x sec (2 x) tan (2 x)

= - \frac{sec ( 2 x )}{x ^{\frac{2}{3}}} - 6 3 x sec (2 x) tan (2 x)

d er i v a t i v e \frac{9 x - 9}{- x + 7}

t an g e n t y = 3 x^{2} - 7 x + 4

\int sec (y) d y

t an g e n t \frac{x ^{2} + 1}{x + e ^{x} + 2}

\int (- x^{2} - 3 x) d x