derivative y=(sec(x))/(1+sec(x))

解答

导数

y = \frac{sec ( x )}{1 + sec ( x )}

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

求解步骤

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

使用微分除法定则:

(\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}}

化简

\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}}

\int 2 x (6 x^{2} - 12)^{2} d x

\frac{d}{d x} (\frac{1 + sin ( x )}{1 - sin ( x )})

d er i v a t i v e f (x) = (x + (x + sin^{2} (x))^{3})^{4}

\int x^{2} cos (21 x) d x

\int_{0}^{5} ∣ 3 - x ∣ d x