Question

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

Answer 1

$\text{Let}{f}^{\prime }\left(x\right)=li{m}_{h\to 0}\frac{f(x+h)-f\left(x\right)}{h}$

$f^{\prime }\left(x\right)=li{m}_{h\to 0}\frac{99(x+y)-99x}{h}$

$=li{m}_{h\to 0}\frac{99x+99h-99x}{h}$

$=li{m}_{h\to 0}\frac{99h}{h}=99$

At x = 100, f'(100) = 99