Find the derivative of f(x) = x at x = 1

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Solution

$Let f^{'} (x) = l i m_{h \to 0} \frac{f (x + y) - f (x)}{h}$

$f'(x) = l i m_{h \to 0} \frac{x + y - x}{h}$

$= l i m_{h \to 0} \frac{h}{h} = 1$

$At x = 1,$ f'(1)=1

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