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प्रश्न
Find the derivative of f (x) = x2 − 2 at x = 10
उत्तर
We have:
\[f'(x) = \lim_{h \to 0} \frac{f(10 + h) - f(10)}{h}\]
\[ = \lim_{h \to 0} \frac{(10 + h )^2 - 2 - ( {10}^2 - 2)}{h}\]
\[ = \lim_{h \to 0} \frac{100 + h^2 + 20h - 2 - 100 + 2}{h}\]
\[ = \lim_{h \to 0} \frac{h^2 + 20h}{h}\]
\[ = \lim_{h \to 0} \frac{h(h + 20)}{h}\]
\[ = \lim_{h \to 0} h + 20\]
\[ = 0 + 20\]
\[ = 20\]
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