Chapter 3: Derivatives - Section 3.2 - The Derivative as a Function - Exercises 3.2 - Page 115: 21

$\dfrac{1}{8}$

Use derivative formula; $f(x)= x^n \implies f'(x)= n x^{n-1}$ Consider $r(x) = \dfrac{2}{\sqrt {(4-x)}}$ Now, $r'(x) = 2(-\dfrac{1}{2})(4-x)^{-3/2}(-1)= (4-x)^{-3/2}$ Then, we have $r'(0) = (4-0)^{-3/2}=2^{-3}= \dfrac{1}{8}$