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Class XI Mathematics

Chapter 12: Limits and Derivatives

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

Example 1

Applying Quotient Rule

Differentiate f(x) = x / (x + 1) with respect to x.
Point P(x, y)Tangent Slope = dy/dx

Calculation Steps:

  1. 1Let u = x (u'=1) and v = x+1 (v'=1).
  2. 2Apply quotient rule: [u'v - uv'] / v².
  3. 3Substitute: [1*(x+1) - x*1] / (x+1)².
  4. 4Simplify: [x + 1 - x] / (x+1)² = 1 / (x+1)².
Solution1 / (x + 1)^2