Question:
Find the derivative of x at x = 1.
Find the derivative of x at x = 1.
Updated On: Oct 25, 2023
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Solution and Explanation
Letf(x) = x. Accordingly,
f'(1) = \(\lim_{h\rightarrow 0}\)\(\frac{f(1+h)-f(1)}{h}\)
= \(\lim_{h\rightarrow 0}\) \(\frac{(1+h)-(1)}{h}\)
= \(\lim_{h\rightarrow 0}\) \(\frac{h}{h}\)
= \(\lim_{h\rightarrow 0}\) (1)
=1
Thus, the derivative of x at x = 1 is 1.
f'(1) = \(\lim_{h\rightarrow 0}\)\(\frac{f(1+h)-f(1)}{h}\)
= \(\lim_{h\rightarrow 0}\) \(\frac{(1+h)-(1)}{h}\)
= \(\lim_{h\rightarrow 0}\) \(\frac{h}{h}\)
= \(\lim_{h\rightarrow 0}\) (1)
=1
Thus, the derivative of x at x = 1 is 1.
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