Exercise 2.8 Class 12 maths || NBF 2025 New Book || ex 2.8 NBF Class 12 maths || By Sir Raaz

Exercise 2.8 – 2nd Year Math | Second Derivative | Higher-Order Derivatives | Complete Solution

In this complete lecture, I have solved all questions from Exercise 2.8 of 2nd Year Mathematics (FSc / ICS Part 2). This exercise focuses on second derivatives, higher-order derivatives, and their algebraic and trigonometric applications.
✅ Second derivative of functions
✅ Derivatives of exponential, logarithmic, trigonometric functions
✅ Applying derivative formulas and rules
✅ Chain rule, product rule, and quotient rule
✅ Using definitions of second derivative from first principles
✅ Finding third derivative using product rule
CHAPTERS:
00:00 Intro
00:23 Q#1
03:01 Q#2
02:28 Q#3
06:28 Q#4
08:30 Q#5
09:27 Q#6
11:05 Q#7
16:56 Q#8
19:43 Q#9
21:25 Q#10
24:20 Q#11
26:57 Q#12
30:41 Q#13
33:25 Q#14
36:03 Q#15
40:00 Q#16
43:18 Q#17
45:38 Q#18
48:45 Q#19
55:05 Q#20
📘 All questions are explained step by step in easy Urdu/Hindi, making it ideal for board exam preparation and entry test revision.Topics Covered:

Second-order derivative (d²y/dx²)

Third-order derivative (d³y/dx³)

Differentiating polynomials, trigonometric, and logarithmic functions

Derivative using first principles

Using general formulas for second derivatives

Derivatives of products (fg) and chain rule applicationsPerfect For:

Class 12 / Grade 12 Students (FSc / ICS Part 2)

Punjab Board / Federal Board / Sindh Board

Entry test students (MDCAT / ECAT)

Students needing clear concepts in calculus
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