derivative of (sec(x)/(1+tan(x)))

Lösung

\frac{d}{d x} (\frac{sec ( x )}{1 + tan ( x )})

\frac{- cos ( x ) + sin ( x )}{1 + sin ( 2 x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{sec ( x )}{1 + tan ( x )})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (1 + tan (x)) = sec^{2} (x)

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

Vereinfache

\frac{sec ( x ) tan ( x ) ( 1 + tan ( x ) ) - sec ^{2} ( x ) sec ( x )}{( 1 + tan ( x ) ) ^{2}} : \frac{- cos ( x ) + sin ( x )}{1 + sin ( 2 x )}

= \frac{- cos ( x ) + sin ( x )}{1 + sin ( 2 x )}

\frac{d}{d x} (- 0.0006 x (x - 15)^{2} (x - 40))

d er i v a t i v e y = x (7 x + 3)^{\frac{1}{3}}

x \to + 0 lim (x^{3} cos (\frac{π}{x}))

\frac{\partial}{\partial x} (sin (2 x y))

\frac{d}{d x} (16 - \frac{1}{625} x^{2})