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

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

$\begin{matrix} \frac{d}{d x} (\frac{x + 1}{x - 1}) & = \frac{(x - 1) \frac{d}{d x} (x + 1) - (x + 1) \frac{d}{d x} (x - 1)}{(x - 1)^{2}} = \frac{(x - 1) (1) - (x + 1) (1)}{(x - 1)^{2}} = \frac{x - 1 - x - 1}{(x - 1)^{2}} = \frac{- 2}{(x - 1)^{2}} \end{matrix}$

Method 2

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