Find the derivative of f(x) = x at x = 1. | vedclass

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(B) Let $f(x) = x$. By the definition of the derivative,$f'(a) = \mathop{\lim}\limits_{h 	o 0} \frac{f(a+h) - f(a)}{h}$. For $a = 1$,we have: $f'(1)

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$1$

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(B) Let $f(x) = x$. By the definition of the derivative,$f'(a) = \mathop{\lim}\limits_{h 	o 0} \frac{f(a+h) - f(a)}{h}$. For $a = 1$,we have: $f'(1) = \mathop{\lim}\limits_{h 	o 0} \frac{f(1+h) - f(1)}{h}$ Since $f(x) = x$,we substitute $f(1+h) = 1+h$ and $f(1) = 1$: $f'(1) = \mathop{\lim}\limits_{h 	o 0} \frac{(1+h) - 1}{h}$ $f'(1) = \mathop{\lim}\limits_{h 	o 0} \frac{h}{h}$ $f'(1) = \mathop{\lim}\limits_{h 	o 0} (1) = 1$. Thus,the derivative of $x$ at $x = 1$ is $1$.

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

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