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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{6 x + 2}{x + 1})

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

\frac{\partial}{\partial x} (x^{2} + 3 yz + 4 x y)

y^{^{'}} = (x y^{^{'}} + y) y^{1} 985

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