Class 12 Math: Continuity and Differentiability Solved Examples & Step Solutions
NexPro Tools Mathematics TeamJune 5, 20266 min read
The best way to gain confidence in mathematics is by studying solved examples. By analyzing how formulas are applied step-by-step, you learn how to tackle complex questions in your homework and exams. Let's walk through standard worked examples for Class 12 Continuity and Differentiability.
Step-by-Step Solved Problems
Example 1: Composite differentiation
Question: Differentiate cos(x²) with respect to x.
Worked Solution Steps:
- Let y = cos(u) where u = x².
- Differentiate y with respect to u: dy/du = -sin(u).
- Differentiate u with respect to x: du/dx = 2x.
- Apply Chain Rule: dy/dx = (dy/du) * (du/dx) = -sin(x²) * 2x.
- State result: -2x sin(x²).
Final Answer: -2x\sin(x^2)
Self-Practice Method
When studying these examples, cover the solution with a sheet of paper and attempt to solve the question on your own. If you get stuck, reveal the steps one by one to identify where your logic deviated. This active recall method builds long-term problem-solving skills.
📚 Class 12 Math Resource Hub for Continuity and Differentiability:
• 🧮 Interactive Solver: Solve Continuity and Differentiability Problems - Verify steps in real-time.
• 📝 Timed Practice Quiz: Take Continuity and Differentiability Online Quiz - Test your speed and concepts.
• 📄 Printable Worksheet: Download Continuity and Differentiability PDF Worksheet - Interactive problems with answers.
• 📐 Formula Sheet: View Continuity and Differentiability Key Equations - Complete revision references.
• 🔄 Next Topic Guide: Integrals Study Notes
• 🎓 Syllabus Overview: Class 12 Mathematics Portal - Access all chapter guides.