Answer: sec²x.
- A sec²x
- B −cosec²x
- C sec x tan x
- D cot x
Correct answer: A. sec²x
Explanation: d(tan x)/dx = sec²x.
f(x)=|x| is perfectly continuous at x=0 (no break, no jump), but the curve has a sharp corner there: approaching from the left gives slope -1 and from the right gives slope +1 - since these one-sided derivatives disagree, the function is not differentiable at that point.
Concept context
When a function has no breaks (continuity) and when it has a well-defined slope (differentiability), plus rules for differentiating implicit, inverse trig, exponential, log, and parametric functions.