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Question
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
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Solution
\[\text{ We have }: \]
\[f'\left( \frac{\pi}{2} \right) = \lim_{h \to 0} \frac{f\left( \frac{\pi}{2} + h \right) - f\left( \frac{\pi}{2} \right)}{h}\]
\[ = \lim_{h \to 0} \frac{2cos\left( \frac{\pi}{2} + h \right) - cos\left( \frac{\pi}{2} \right)}{h}\]
\[ = \lim_{h \to 0} \frac{- 2sin h - 0}{h}\]
\[ = - 2 \lim_{h \to 0} \frac{\sinh}{h}\]
\[ = - 2(1)\]
\[ = - 2\]
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