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Class XII Mathematics

Chapter 5: Continuity and Differentiability

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

Example 1

Composite differentiation

Differentiate cos(x²) with respect to x.
Point P(x, y)Tangent Slope = dy/dx

Calculation Steps:

  1. 1Let y = cos(u) where u = x².
  2. 2Differentiate y with respect to u: dy/du = -sin(u).
  3. 3Differentiate u with respect to x: du/dx = 2x.
  4. 4Apply Chain Rule: dy/dx = (dy/du) * (du/dx) = -sin(x²) * 2x.
  5. 5State result: -2x sin(x²).
Solution-2x\sin(x^2)