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.