PART 5：正割、餘割函數的微分定理&證明

定理7
\(f(x) = \sec x\) ，則 \({f^\prime }(x) = \sec x\tan x\)

證明
\(f(x) = \sec x = \frac{1}{{\cos x}}\) ，利用除法的微分公式，
則 \(f'(x) = \frac{{0 \cdot \cos x - 1 \cdot {{\left( {\cos x} \right)}^\prime }}}{{{{\cos }^2}x}} = \frac{1}{{\cos x}} \cdot \frac{{\sin x}}{{\cos x}}\)
\( = \sec x \cdot \tan x\)
定理8
\(f(x) = \csc x\) ，則 \({f^\prime }(x) = -\csc x\cot x\)

證明
\(f(x) = \csc x = \frac{1}{{\sin x}}\)，利用除法的微分公式，
則 \(f'(x) = \frac{{0 \cdot \sin x - 1 \cdot {{\left( {\sin x} \right)}^\prime }}}{{{{\sin }^2}x}} = \frac{{ - 1}}{{\sin x}} \cdot \frac{{\cos x}}{{\sin x}}\)
\( =  - \csc x \cdot \cot x\)