derivative of (tan(x-4)/(sec(x)))

解答

\frac{d}{d x} (\frac{tan ( x ) - 4}{sec ( x )})

\frac{sec ^{2} ( x ) - tan ( x ) ( tan ( x ) - 4 )}{sec ( x )}

求解步骤

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

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

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

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

化简

\frac{sec ^{2} ( x ) sec ( x ) - sec ( x ) tan ( x ) ( tan ( x ) - 4 )}{sec ^{2} ( x )} : \frac{sec ^{2} ( x ) - tan ( x ) ( tan ( x ) - 4 )}{sec ( x )}

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

\frac{\partial}{\partial x} (e^{- 5 x})

d er i v a t i v e 2 ln (cos (x))

4 y^{^{''}} = y

y^{^{'}} = - 3 y

\frac{d}{d x} (ln (2 x - y))