derivative f(x)=(tan(9x))/(1+sin(9x))

解答

导数

f (x) = \frac{tan ( 9 x )}{1 + sin ( 9 x )}

\frac{- 9 sin ( 9 x ) + 9 sec ^{2} ( 9 x ) ( 1 + sin ( 9 x ) )}{( 1 + sin ( 9 x ) ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{tan ( 9 x )}{1 + sin ( 9 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 ( 9 x ) ) ( 1 + sin ( 9 x ) ) - \frac{d}{d x} ( 1 + sin ( 9 x ) ) tan ( 9 x )}{( 1 + sin ( 9 x ) ) ^{2}}

\frac{d}{d x} (tan (9 x)) = sec^{2} (9 x) \cdot 9

\frac{d}{d x} (1 + sin (9 x)) = 9 cos (9 x)

= \frac{sec ^{2} ( 9 x ) \cdot 9 ( 1 + sin ( 9 x ) ) - 9 cos ( 9 x ) tan ( 9 x )}{( 1 + sin ( 9 x ) ) ^{2}}

cos (9 x) tan (9 x) = sin (9 x)

= \frac{- 9 sin ( 9 x ) + 9 sec ^{2} ( 9 x ) ( 1 + sin ( 9 x ) )}{( 1 + sin ( 9 x ) ) ^{2}}

(2 x + 3 y - 1) d x - 4 (x + 1) d y = 0

in v erse l a pl a ce \frac{e ^{- 2 s}}{s ( s - 2 )}

\frac{d}{d x} (- 2 e^{5 y} x - 2 sin (2 x))

\int_{- 2}^{2} (4 - x^{2}) d x

t a y l or (1 - x^{2})^{\frac{1}{2}}