To determine the derivative of the functions from first principles, we use the definition:
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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, $f(x) = \sec x = \frac{1}{\cos x}$.
$$f'(x) = \lim_{h \to 0} \frac{\sec(x+h) - \sec x}{h}$$
$$f'(x) = \lim_{h \to 0} \frac{\frac{1}{\cos(x+h)} - \frac{1}{\cos x}}{h}$$
$$f'(x) = \lim_{
