Given the function h(x) = |x|, find the derivative h'(x) for x ≠ 0.
To find the derivative of h(x) = |x|, we can first rewrite the absolute value function as a piecewise function:

h(x) = { x  if x ≥ 0
         {-x if x < 0

Now, we can find the derivative for each case separately.

For x > 0, h(x) = x, so h'(x) = 1.
For x < 0, h(x) = -x, so h'(x) = -1.

Thus, the derivative h'(x) is also a piecewise function:

h'(x) = { 1  if x > 0
          {-1 if x < 0