# Find the Derivative of the Following Function at the Indicated Point: 2 Cos X at X = π 2 - Mathematics

Find the derivative of the following function at the indicated point:

2 cos x at x =$\frac{\pi}{2}$

#### 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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.1 | Q 7.3 | Page 3