Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the derivative of the following functions from first principle. x + 1 x -1

4.(iv)     Find the derivative of the following functions from first principle. \frac{x +1}{x-1}

Answers (1)

best_answer

Given:

f(x)=\frac{x +1}{x-1}

Now, As we know, The derivative of any function at x is 

f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}

f'(x)=\lim_{h\rightarrow 0}\frac{\frac{x+h+1}{x+h-1}-\frac{x+1}{x-1}}{h}

f'(x)=\lim_{h\rightarrow 0}\frac{\frac{(x+h+1)(x-1)-(x+1)(x+h-1)}{(x-1)(x+h-1)}}{h}

f'(x)=\lim_{h\rightarrow 0}\frac{x^2-x+hx-h+x-1-x^2-xh+x-x-h+1}{(x-1)(x+h-1)h}

f'(x)=\lim_{h\rightarrow 0}\frac{-2h}{(x-1)(x+h-1)h}

f'(x)=\lim_{h\rightarrow 0}\frac{-2}{(x-1)(x+h-1)}

f'(x)=\frac{-2}{(x-1)(x+0-1)}

f'(x)=\frac{-2}{(x-1)^2}  (Answer)

Posted by

Pankaj Sanodiya

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question