Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find dy/dx of the functions given in Exercises 12 to 15. x y = e^x -y

 Q15  Find dy/dx of the functions given in Exercises 12 to 15.  xy = e ^{x-y}

 

Answers (1)

best_answer

Given function is
f(x)\Rightarrow xy = e ^{x-y}
Now, take  take log on both the sides
\log x+\ log y = (x-y)(1) \ \ \ \ \ \ \ \ \ \ \ \ (\because \log e = 1)\\ \log x+\ log y = (x-y)
Now, differentiate w.r.t  x
\frac{1}{x}+\frac{1}{y}\frac{dy}{dx}=1-\frac{dy}{dx}
By taking similar terms on same side
We get, 
(\frac{1}{y}+1)\frac{dy}{dx}=1-\frac{1}{x}\\ \frac{y+1}{y}.\frac{dy}{dx}= \frac{x-1}{x}\\ \frac{dy}{dx}= \frac{y}{x}.\frac{x-1}{y+1}
Therefore, the answer is  \frac{y}{x}.\frac{x-1}{y+1} 

Posted by

Gautam harsolia

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

‘Careers are at stake’: CBSE removes additional subject option for private students without prior notice
anam-khan

CBSE eases APAAR ID mandate for board exams 2026 over lack of parental consent, technical issues
anam-khan

CBSE Board 2026: Exam form submission for Class 10, 12 private students begins tomorrow

Latest Question