derivative of (cos(x)/x+x/(cos(x)))

解答

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

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

求解步骤

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

化简

\frac{cos ( x )}{x} + \frac{x}{cos ( x )} : \frac{cos ( x )}{x} + x sec (x)

= \frac{d}{d x} (\frac{cos ( x )}{x} + x sec (x))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{cos ( x )}{x}) + \frac{d}{d x} (x sec (x))

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

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

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

d er i v a t i v e \frac{1}{4 x ^{2} + 1}

x \to 0 + lim (\frac{x ^{2}}{9} - \frac{2}{x})

\int \frac{1}{x ^{\frac{1}{2}} + x ^{\frac{3}{2}}} d x

t an g e n t f (x) = - 5 - 2 x^{2}, (- 3, - 23)

y^{^{'}} + e^{x} y = 2 e^{x}