Question

Find the derivative of 99x at x = 100.

Answer 1

${\displaystyle f\prime \left(a\right)=\underset{x\to a}{lim}\frac{f(a+h)-f\left(a\right)}{h}}$

${\displaystyle f\prime \left(100\right)=\underset{h\to 0}{lim}\frac{99(100+h)-99\times 100}{h}}$

= ${\displaystyle \underset{h\to 0}{lim}\frac{99\times 100+99h-99\times 100}{h}}$

= ${\displaystyle =\underset{h\to 0}{lim}\frac{99\times h}{h}}$

= 99