Class 11 RD Sharma Solutions Chapter 30 - Derivatives (Ex 30.2)Free PDF
FAQs on RD Sharma Class 11 Solutions Chapter 30 - Derivatives (Ex 30.2) Exercise 30.2
1. Where can I find accurate, step-by-step solutions for all questions in RD Sharma Class 11 Maths Chapter 30, Exercise 30.2?
You can find reliable and detailed solutions for every problem in RD Sharma Class 11 Maths Chapter 30, Exercise 30.2, on Vedantu. These solutions are crafted by expert educators to ensure they follow the correct methodology and are aligned with the 2025-26 CBSE curriculum, helping you understand the steps to reach the correct answer.
2. What is the primary method used for solving problems in RD Sharma Class 11 Maths Ex 30.2?
Exercise 30.2 primarily focuses on calculating the derivative of functions from the first principle, also known as the delta method or ab-initio method. The solutions demonstrate how to apply the limit definition of a derivative, which is f'(x) = lim (h→0) [f(x+h) - f(x)] / h, to various types of functions.
3. Can you provide a step-by-step guide to finding the derivative of a function like f(x) = x³ using the method from Exercise 30.2?
Certainly. To solve for the derivative of f(x) = x³ using the first principle as shown in Ex 30.2 solutions, you would follow these steps:
- First, identify f(x) = x³ and determine f(x+h) = (x+h)³.
- Use the binomial expansion for (x+h)³ which is x³ + 3x²h + 3xh² + h³.
- Substitute these into the first principle formula: lim (h→0) [ (x³ + 3x²h + 3xh² + h³) - x³ ] / h.
- Simplify the numerator to get 3x²h + 3xh² + h³.
- Factor out 'h' from the numerator: h(3x² + 3xh + h²).
- Cancel 'h' from the numerator and denominator.
- Finally, apply the limit by substituting h = 0 into (3x² + 3xh + h²), which results in the derivative 3x².
4. What is a common mistake students make when solving questions from Exercise 30.2?
A very common mistake is an error in algebraic expansion of the f(x+h) term, particularly with polynomials or rational functions. Another frequent pitfall is trying to substitute h=0 before simplifying the expression, which leads to an indeterminate form (0/0). It is crucial to algebraically manipulate the expression to cancel the 'h' in the denominator before applying the limit.
5. Why is it important to master the first principle method in Ex 30.2, even when direct differentiation formulas exist?
Mastering the first principle is fundamental because it reveals the conceptual origin of derivatives. It demonstrates that a derivative is the limit of the average rate of change. While direct formulas are shortcuts for computation, understanding the first principle provides the 'why' behind those rules and is essential for grasping more complex topics in calculus and its applications in physics and other sciences.
6. How does solving problems in Exercise 30.2 help in understanding the graphical meaning of a derivative?
The expression [f(x+h) - f(x)] / h in the first principle formula represents the slope of a secant line cutting the function's graph at two points. By taking the limit as h → 0, you are essentially finding the slope of that line at a single point. Therefore, solving problems in Ex 30.2 directly reinforces the geometric interpretation that the derivative at a point is the slope of the tangent line to the curve at that point.
7. How can I verify if my answer for a problem in RD Sharma Exercise 30.2 is correct?
A quick way to verify your answer, after solving it using the first principle, is to apply the standard differentiation formulas you may learn later. For instance, if you found the derivative of x³ to be 3x² using the first principle, you can confirm it with the power rule (d/dx(xⁿ) = nxⁿ⁻¹). If the results match, your step-by-step solution is most likely correct.
