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📐 Mathematics  ·  Continuity and Differentiability  ·  JEE

The chain rule is used to differentiate a ___ function:

Answer: composite.

  • A composite
  • B constant
  • C linear-only
  • D polynomial-only

Correct answer: A. composite

Explanation: The chain rule handles composite functions of the form f(g(x)).

f(x) = |x|: Continuous but NOT Differentiable at 0x=0 (sharp "kink")LHD = -1RHD = +1LHD ≠ RHD at the kink → not differentiable, even though the curve has no gap (continuous)

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.

Read the full Continuity and Differentiability notes →