Question

Find the derivative of 99x at x = 100.

Answer 1

Let f(x) = 99x. Accordingly,
f'(100) = $\lim_{h\rightarrow 0}$ $\frac{f(100+h)-f(100)}{h}$
=$\lim_{h\rightarrow 0}$ $\frac{99(100+h)-99(100)}{h}$
=$\lim_{h\rightarrow 0}$ $\frac{99\times100+99h-99\times 100}{h}$
=$\lim_{h\rightarrow 0}$ $\frac{99h}{h}$
=$\lim_{h\rightarrow 0}$ (99) = 99
Thus, the derivative of 99x at x = 100 is 99.