Question

Find the derivative of x at x = 1.

Answer 1

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.