Question

Find the derivative of f (x) = 99x at x = 100

Answer 1

We have:
$$\begin{gathered} f\text{'}\left(100\right)=\underset{h\to 0}{\lim }\frac{f(100+h)-f\left(100\right)}{h} \\ =\underset{h\to 0}{\lim }\frac{99(100+h)-99\left(100\right)}{h} \\ =\underset{h\to 0}{\lim }\frac{9900+99h-9900}{h} \\ =\underset{h\to 0}{\lim }\frac{99h}{h} \\ =\underset{h\to 0}{\lim }99 \\ =99 \end{gathered}$$