To determine the derivative of the functions from first principles, we use the definition:

To determine the derivative of the functions from first principles, we use the definition:

$$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$

a) $y = \sec x$
Here, $f(x) = \sec x = \frac{1}{\cos x}$.

$$f'(x) = \lim_{h \to 0} \frac{\sec(x+h) - \sec x}{h}$$ $$f'(x) = \lim_{h \to 0} \frac{\frac{1}{\cos(x+h)} - \frac{1}{\cos x}}{h}$$ $$$$