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Find the Derivative of F (X) = Cos X at X = 0 - Mathematics

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Find the derivative of f (x) = cos x at x = 0

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Solution

We have: 

\[f'(x) = \lim_{h \to 0} \frac{f(0 + h) - f(0)}{h}\]
\[ = \lim_{h \to 0} \frac{f(h) - f(0)}{h}\]
\[ = \lim_{h \to 0} \frac{\cosh - \cos0}{h}\]
\[ = \lim_{h \to 0} \frac{\cosh - 1}{h}\]
\[ {= \lim}_{h \to 0} \frac{- 2 \sin^2 \frac{h}{2}}{h}\]
\[ {= \lim_{h \to 0} \frac{- 2 \sin^2 \frac{h}{2}}{\frac{h^2}{4}}}_{} \times \frac{h}{4}\]
\[ = {= \lim_{h \to 0} - 1}_{} \times \frac{h}{2}\]
\[ = 0\]

 

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.1 | Q 5 | Page 3

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