Differentiate the following from first principle: 2x+3 x-2 - Vidyadip

Question

Differentiate the following from first principle:$\frac{\text{2x}+3}{\text{x}-2}$

✓

Answer

We have, $\text{f(x)}=\frac{2\text{x}+3}{\text{x}-2}$ $\therefore\text{f}'\text{(x)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(a+h)}-\text{f(a)}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\Big(\frac{2\text{x}+2\text{h}+3}{\text{x+h}-2}\Big)-\Big(\frac{2\text{x}+3}{\text{x}-2}\Big)}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{2\text{x}^2+2\text{xh}+3\text{x}-4\text{x}-4\text{h}-6-2\text{x}^2-2\text{hx}+4\text{x}-3\text{x}-3\text{h}+6}{\text{h}(\text{x+h}-2)(\text{x}-2)}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{-7}{(\text{x+h}-2)(\text{x}-2)}$ $=\frac{-7}{(\text{x}-2)^2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from Derivatives→Derivatives — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Which of the following are ture. (2 × 3)! = 2! × 3!

If the sum of n terms of an A.P. is $\text{np}+\frac{1}{2}\text{n}(\text{n}-1)$ Q, where P and Q are constants, find the common difference.

All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other:

In a survey of 100 persons it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A and B, 10 read magazines A and C, 5 read magazines B and C and 3 read all the three magazines?

How many read none of three magazines?
How many read magazine C only?

Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes Equal in magnitude and both positive,Equal in magnitude but opposite in sign.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$36x^2 + 4y^2 = 144$

If f is a function satisfying f (x+y) = f (x) f (y) for all x, y $ \in $ N such that f (1) = 3 and $\sum\limits_{x = 1}^n f (x) = 120$ find the value of n.

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine
(i) P (not A) (ii) P (not B) and (iii) P (A or B)

Let $X=\{1,2,3,4\}$ and $Y=\{1,5,9,11,15,16\}$. Determine which of the following sets are functions from $X$ to $Y: f_3=$ $\{(1,5),(2,9),(3,1),(4,5),(2,11)\}$

Find the values of the following expressions: $\text{i}^{5}+\text{i}^{10}+\text{i}^{15}$