PART 4：正切、餘切函數的微分(03:22)

定理5
\(f(x) = \tan x\)，則 \({f^\prime }(x) = {\sec ^2}x\)
證明:  \(f(x) = \tan x = \frac{{\sin x}}{{\cos x}}\) ，利用除法的微分公式，
則 \({f^\prime }(x) = \frac{{{{\left( {\sin x} \right)}^\prime }\left( {\cos x} \right) - \left( {\sin x} \right){{\left( {\cos x} \right)}^\prime }}}{{{{\cos }^2}x}}\)
\( = \frac{{\left( {\cos x} \right)\left( {\cos x} \right) - \left( {\sin x} \right)\left( { - \sin x} \right)}}{{{{\cos }^2}x}}\)
\( = \frac{1}{{{{\cos }^2}x}} = {\sec ^2}x\)
定理6
\(f(x) = \cot x\)，則 \({f^\prime }(x) =  - {\csc ^2}x\)
(證明方法一樣，同學可自行練習)