Mathematics

Problem

Let

f(x)=\arccos(2x)

for

x

\left[-\dfrac{1}{2},\dfrac{1}{2}\right]

. Answer the following questions. (a) Derive an explicit expression for

f'(x)

in terms of

x

. (b) Evaluate

f'(x)

x=\dfrac{\sqrt{3}}{4}

, showing each substitution step before simplifying. (c) Write the exact simplified value of

f'\!\left(\dfrac{\sqrt{3}}{4}\right)