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

解答

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

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

求解步骤

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

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

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

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

d er i v a t i v e e^{8 x y}

d er i v a t i v e sin (x) \cdot cos (x)

d er i v a t i v e (1.01)^{x} + 0.3 3^{x}

\frac{d}{d r} (\frac{2 k}{r} + 2 π r^{2})

(y^{2} + 9) d x - \frac{1}{( 2 x + 1 ) ^{2}} d y = 0