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NCERT Class 12 · Ch 5 Miscellaneous Exercise · Q21

NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Miscellaneous Exercise Question 21

If y=det [[f(x),g(x),h(x)],[l,m,n],[a,b,c]], with l,m,n,a,b,c constants, prove y′=det [[f′(x),g′(x),h′(x)],[l,m,n],[a,b,c]].

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: The derivative is the stated first-row derivative determinant.
  1. Expand along the first row: y=f(x)(mc−nb)−g(x)(lc−na)+h(x)(lb−ma).
  2. The three cofactors are constants. Differentiate termwise to get f′(mc−nb)−g′(lc−na)+h′(lb−ma), the determinant on the right.

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