derivative of-2/(cos(2x)+8/3)

Lösung

\frac{d}{d x} (- \frac{2}{cos ( 2 x )} + \frac{8}{3})

- 4 sec (2 x) tan (2 x)

Schritte zur Lösung

\frac{d}{d x} (- \frac{2}{cos ( 2 x )} + \frac{8}{3})

Vereinfache

- \frac{2}{cos ( 2 x )} + \frac{8}{3} : - 2 sec (2 x) + \frac{8}{3}

= \frac{d}{d x} (- 2 sec (2 x) + \frac{8}{3})

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (2 sec (2 x)) + \frac{d}{d x} (\frac{8}{3})

\frac{d}{d x} (2 sec (2 x)) = 4 sec (2 x) tan (2 x)

\frac{d}{d x} (\frac{8}{3}) = 0

= - 4 sec (2 x) tan (2 x) + 0

Vereinfache

= - 4 sec (2 x) tan (2 x)

\frac{\partial}{\partial x} (9 x^{2} cos (y^{6}))

\frac{d}{d x} (\frac{5 x ^{4} + 2 x}{2 x ^{9}})

\int \frac{5 ^{x}}{5 ^{x} - 1} d x

x \to 0 lim (\frac{( 4 + x ) - 16}{x})

d er i v a t i v e f (x) = \frac{5}{6 x ^{5}}