Use your derivative tools to write the second derivative, $\large\frac { d ^ { 2 } y } { d x ^ { 2 } }$, of each function below.

1. $y=\frac{\sin(x)}{x}$ 

   Hint (a):

   Start with the quotient Rule.

2. $y=\csc^2\left(x\right)-\cot^2\left(x\right)$ 

   Hint (b):

   Use the chain rule.

3. $y=\sqrt{\frac{1}{x}}$ 

   Hint (c):

   You could use the quotient rule AND the chain rule...Or you could rewrite y as with exponents and quickly use the Power Rule!

4. $y=|x-2|$ 

   Hint (d):

   Rewrite y as a piecewise function. The derivative will be a piecewise function as well. So will the second derivative.