Verify the function is defined at the point of interest
Check continuity at the point
Compute the left-hand derivative, if applicable
Compute the right-hand derivative, if applicable
Compare the left-hand and right-hand derivatives
Confirm both one-sided derivatives exist and are equal
Ensure the derivative is finite
Check for corners, cusps, vertical tangents, or jumps
For piecewise functions, test differentiability at each boundary point
Use the limit definition of the derivative
Confirm the limit of the difference quotient exists
Check whether the function is differentiable on an interval by testing every point in the interval