f(x) = sec(x)
f(x) = 1
cos(x)
[tex]\frac{f(x + \delta x) - f(x)}{\delta x} = \frac{(1 + \delta x) - 1}{\delta x}[/tex]
[tex]\frac{f(x + \delta x) - f(x)}{\delta x} = \frac{1 - 1 + \delta x}{\delta x}[/tex]
[tex]\frac{f(x + \delta x) - f(x)}{\delta x} = \frac{\delta x}{\delta x}[/tex]
[tex]\frac{f(x + \delta x) - f(x)}{\delta x} = 1[/tex]
[tex]\frac{f(x + \delta x) - f(x)}{\delta x} = -sin(x)[/tex]
[tex]sec(x)' = \frac{1}{-sin(x)}[/tex]
[tex]sec(x)' = -csc(x)[/tex]
