derivative ((cos^3(x)-1))/(cos^2(x))

解答

导数

\frac{( cos ^{3} ( x ) - 1 )}{cos ^{2} ( x )}

\frac{- 3 cos ^{4} ( x ) sin ( x ) + sin ( 2 x ) ( cos ^{3} ( x ) - 1 )}{cos ^{4} ( x )}

求解步骤

\frac{d}{d x} (\frac{cos ^{3} ( x ) - 1}{cos ^{2} ( 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} ( cos ^{3} ( x ) - 1 ) cos ^{2} ( x ) - \frac{d}{d x} ( cos ^{2} ( x ) ) ( cos ^{3} ( x ) - 1 )}{( cos ^{2} ( x ) ) ^{2}}

\frac{d}{d x} (cos^{3} (x) - 1) = - 3 cos^{2} (x) sin (x)

\frac{d}{d x} (cos^{2} (x)) = - sin (2 x)

= \frac{( - 3 cos ^{2} ( x ) sin ( x ) ) cos ^{2} ( x ) - ( - sin ( 2 x ) ) ( cos ^{3} ( x ) - 1 )}{( cos ^{2} ( x ) ) ^{2}}

化简

\frac{( - 3 cos ^{2} ( x ) sin ( x ) ) cos ^{2} ( x ) - ( - sin ( 2 x ) ) ( cos ^{3} ( x ) - 1 )}{( cos ^{2} ( x ) ) ^{2}} : \frac{- 3 cos ^{4} ( x ) sin ( x ) + sin ( 2 x ) ( cos ^{3} ( x ) - 1 )}{cos ^{4} ( x )}

= \frac{- 3 cos ^{4} ( x ) sin ( x ) + sin ( 2 x ) ( cos ^{3} ( x ) - 1 )}{cos ^{4} ( x )}

11 (t + 1) y^{^{'}} - 9 y = 18 t

\frac{d}{d x} (\frac{x}{x + \frac{b}{x}})

\frac{\partial}{\partial x} (e^{x^{2 - y^{2}}})

d er i v a t i v e y = ln (30) + 3 0^{x + 4}

\int 3 x - 8 d x