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Question
Find the derivative of f (x) = tan x at x = 0
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Solution
We have:
\[f'(x) = \lim_{h \to 0} \frac{f(0 + h) - f(0)}{h}\]
\[ = \lim_{h \to 0} \frac{f(h) - f(0)}{h}\]
\[ = \lim_{h \to 0} \frac{\tanh - \tan0}{h}\]
\[ = \lim_{h \to 0} \frac{\tanh}{h}\]
\[ = 1\]
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