Q81.For x > 1, if (2x)2y = 4e2x−2y , then (1 + loge 2x)2 dxdy is equal to (1) loge2x (2) xloge2x−loge2x (3) xloge2x (4) xloge2x+loge2x
What This Question Tests
The problem involves differentiating an implicitly defined function using logarithms and then algebraic manipulation to isolate the required derivative expression. A crucial simplification step is to first take logarithm on both sides of the given equation.
Concepts Tested
Formulas Used
d/dx(log u) = (1/u)du/dx
Chain rule
📚 NCERT Sections This Tests
3.9 — A Reaction Is First Order In A And Second Order In B.
Chemistry Class 11 · Chapter 3
3.9 A reaction is first order in A and second order in B. (i) Write the differential rate equation. (ii) How is the rate affected on increasing the concentration of B three times? (iii) How is the rate affected when the concentrations of both A and B are doubled? 85 Chemical Kinetics Reprint 2025-26
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
📋 Question Details
- Chapter
- Differentiation
- Topic
- Implicit differentiation
- Year
- 2019
- Shift
- 12 Jan Shift 1
- Q Number
- Q81
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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