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Find the Derivative of F (X) = X2 − 2 at X = 10 - Mathematics

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Find the derivative of f (x) = x2 − 2 at x = 10

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Solution

We have:

\[f'(x) = \lim_{h \to 0} \frac{f(10 + h) - f(10)}{h}\]
\[ = \lim_{h \to 0} \frac{(10 + h )^2 - 2 - ( {10}^2 - 2)}{h}\]
\[ = \lim_{h \to 0} \frac{100 + h^2 + 20h - 2 - 100 + 2}{h}\]
\[ = \lim_{h \to 0} \frac{h^2 + 20h}{h}\]
\[ = \lim_{h \to 0} \frac{h(h + 20)}{h}\]
\[ = \lim_{h \to 0} h + 20\]
\[ = 0 + 20\]
\[ = 20\]

 
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 2 | Page 3

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