Fsc 2nd Year Math Notes

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Fsc 2nd Year Math Notes

Math City Fsc Part 2
2nd Year Chemistry Notes
Math City 2nd Year
Math Notes 2nd Year Fsc 2.8
Math City Fsc
Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.
Here are few online resource, which are very helpful to find derivative. Scherl and roth violin serial number.
Contents & summary Average Rate of Change
 Finding $f'(x)$ from Definition of Derivative
 Exercise 2.1
 Exercise 2.2
 Exercise 2.3
 Derivatives of Inverse Function
 Derivative of a Function given in form of parametric Equations
 Exercise 2.4
 Derivatives of Inverse Trigonometric Functions
 Derivative of Exponential Functions
 Logarithmic Differentiation
 Derivative of the Inverse Hyperbolic Function 
 Successive Differentiation ( or Derivatives)
 Series Expansions of Function
 Exercise 2.8
 Increasing and Decreasing Function
 Critical Values and Critical Points
 Exercise 2.10
Mar 03, 2019 These Mathematics-XII FSc Part 2 (2nd year) Notes are according to 'Punjab Text Book Board, Lahore'. There are seven units in this book and we have to work hard to make easy and suitable solutions for students and teachers so that it helps them learn things quickly and easily. Fsc Part 2 Math Notes. Exercise 2.5 (Solution)  Mathematics 2nd Year. By Khurram Farooq Last updated Sep 13, 2018. Share Facebook Twitter Google+ ReddIt WhatsApp. FSc Part 2 (Mathematics): PTB Calculus and Analytic Geometry, MATHEMATICS 12 Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore, Pakistan. There are total seven (7) units in this book. One this page we have posted Notes (Solutions), MCQs, short question, sample papers and old papers related to this subject.
2nd Year Math Notes The understudies of F.Sc Part 2 (Pre Engineering) read the Calculus And Analytic Geometry Mathematics book in their 2-year term which has been distributed by Punjab course reading board Lahore. This is the post on the topic of the 2nd Year Maths Chapter 2 Notes Differentiation pdf. The post is tagged and categorized under in 12th Maths fsc, Education News Tags. For more content related to this post you can click on labels link.
Which method is betterIn this chapter many questions can be solved in much easier way. Actually in every exercise some formula/method is introduced to solve the question. In examination it is not necessary to do the same method as given in exercise. Here is one example:
We have to find the derivative of $frac{x+1}{x-1}$ with respect to $x$.
Method 1

$$begin{aligned}frac{d}{dx}left(frac{x+1}{x-1}right) &= frac{(x-1)frac{d}{dx}(x+1)-(x+1)frac{d}{dx}(x-1)}{(x-1)^2}&= frac{(x-1)(1)-(x+1)(1)}{(x-1)^2}&= frac{x-1-x-1}{(x-1)^2}&= frac{-2}{(x-1)^2}end{aligned}$$
Method 2By converting improper to proper fraction $$frac{x+1}{x-1}= 1+frac{2}{x-1}=1+2(x-1)^{-1}$$Now$$begin{aligned}frac{d}{dx}left(frac{x+1}{x-1}right) &=frac{d}{dx}left(1+2(x-1)^{-1}right)&= 0-2(x-1)^{-2}(1)&= frac{-2}{(x-1)^2}end{aligned}$$
This was a simple example but try it to find the derivative of $frac{x^2+1}{x^2-1}$.
Finding a derivative is not a difficult thing. It has few rules and formulas. Instead of learning sums try to understand the rules for differentiation. Also remember derivative of important function. To remember the derivative just take a print of Important Derivatives & Integrals. At the time of solving question, use this page to see formulas. This method will help to put these formulas in your mind without any trouble. 

$Math notes 2nd year fsc 2.8$

Solutions Exercise 2.1 | View Online | Download PDF (156KB) 

$Fsc 2nd year math notes youtube chapter no 6$

$$begin{aligned}frac{d}{dx}left(frac{x+1}{x-1}right) &= frac{(x-1)frac{d}{dx}(x+1)-(x+1)frac{d}{dx}(x-1)}{(x-1)^2}&= frac{(x-1)(1)-(x+1)(1)}{(x-1)^2}&= frac{x-1-x-1}{(x-1)^2}&= frac{-2}{(x-1)^2}end{aligned}$$
Method 2By converting improper to proper fraction $$frac{x+1}{x-1}= 1+frac{2}{x-1}=1+2(x-1)^{-1}$$Now$$begin{aligned}frac{d}{dx}left(frac{x+1}{x-1}right) &=frac{d}{dx}left(1+2(x-1)^{-1}right)&= 0-2(x-1)^{-2}(1)&= frac{-2}{(x-1)^2}end{aligned}$$
This was a simple example but try it to find the derivative of $frac{x^2+1}{x^2-1}$.
Finding a derivative is not a difficult thing. It has few rules and formulas. Instead of learning sums try to understand the rules for differentiation. Also remember derivative of important function. To remember the derivative just take a print of Important Derivatives & Integrals. At the time of solving question, use this page to see formulas. This method will help to put these formulas in your mind without any trouble. 
Solutions Exercise 2.1 | View Online | Download PDF (156KB) 
 Exercise 2.2 | View Online | Download PDF (130KB)
 Exercise 2.3 | View Online | Download PDF (209KB)
 Exercise 2.4 | View Online | Download PDF (175KB) 
 Exercise 2.5 | View Online | Download PDF (239KB) 
 Exercise 2.6 | View Online | Download PDF (236KB)
 Exercise 2.7 | View Online | Download PDF (194KB)
Math City Fsc Part 2 Exercise 2.8 | View Online | Download PDF (147KB)
2nd Year Chemistry Notes Exercise 2.9 | View Online | Download PDF (200KB)
 Exercise 2.10 | View Online | Download PDF (180KB)
The following notes was written and sent by Mr. Amir Shehzad.
Unit 02: Differentiation | Download PDF (1.53 MB) 
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