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

解答

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

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

求解步骤

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

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

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

\frac{d}{d x} (cos (x) - 4) = - sin (x)

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

化简

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

n = 1 \sum \infty - \frac{5}{2 ^{n - 1}}

\int (x + π) d x

in v erse l a pl a ce F (s) = \frac{( s + 2 ) ^{2}}{s ^{3}}

d er i v a t i v e y = (x^{2} - 8 x) e^{x}

d er i v a t i v e f (x) = \frac{2 x - 4}{x + 1}