derivative of tan(x-sec(x))

解答

\frac{d}{d x} (tan (x) - sec (x))

\frac{1}{1 + sin ( x )}

求解步骤

\frac{d}{d x} (tan (x) - sec (x))

使用微分加减法定则:

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

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

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

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

= sec^{2} (x) - sec (x) tan (x)

化简

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

= \frac{1}{1 + sin ( x )}

\frac{\partial}{\partial x} (x^{3} + y^{3} - 9 x y)

x \to \frac{π}{4} lim (tan (x))

d er i v a t i v e \frac{x}{x + 9}

t an g e n t y = e^{- 4 t}, at t = 0

d er i v a t i v e \frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )}