2nd year chapter 2 Differentiation Notes |Important question

      2nd Year Math Chapter 2 Notes 

Unit no :2

Differentiation  

These notes are available to view or download. These notes covers chapter no three of first year chapter name “ Differentiation”  “these notes cover the following topics 

Which method is better

In 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

$$\begin{array}{cc}\frac{d}{dx}\left(\frac{x+1}{x-1}\right)& =\frac{(x-1)\frac{d}{dx}(x+1)-(x+1)\frac{d}{dx}(x-1)}{(x-1{)}^2}\\ & =\frac{(x-1)\left(1\right)-(x+1)\left(1\right)}{(x-1{)}^2}\\ & =\frac{x-1-x-1}{(x-1{)}^2}\\ & =\frac{-2}{(x-1{)}^2}\end{array}$$

Method 2

By converting improper to proper fraction $$\frac{x+1}{x-1}=1+\frac{2}{x-1}=1+2(x-1{)}^{-1}$$Now$$\begin{array}{cc}\frac{d}{dx}\left(\frac{x+1}{x-1}\right)& =\frac{d}{dx}(1+2(x-1{)}^{-1})\\ & =0-2(x-1{)}^{-2}(1)\\ & =\frac{-2}{(x-1{)}^2}\end{array}$$

This was a simple example but try it to find the derivative of $\frac{x^2+1}{x^2-1}$

FSC/2nd year Math Chapter No.2 

contains a total of ten exercises. These aree 
Important question of this chapter is 

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1st year chapter 1 important questions 

1st year chapter 2 important questions 

1st year chapter 3 important questions

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2nd year chapter 1 important Questions

2nd year chapter 2 Important questions 

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