Answer
$\frac{1}{32}$
Work Step by Step
$\lim\limits_{h \to 0}\frac{\sqrt[4] {16+h}-2}{h}$
This is an expression for the derivative of $f(x) = x^{1/4}$ evaluated at the point $x = 16$
We can evaluate the derivative:
$f(x) = x^{1/4}$
$f'(x) = \frac{1}{4x^{3/4}}$
$f'(16) = \frac{1}{4(16)^{3/4}}$
$f'(16) = \frac{1}{4(8)}$
$f'(16) = \frac{1}{32}$
