Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

If \log(x^2 + y^2) = 2\tan^{-1}\left (\frac{y}{x} \right ), show that \frac{dy}{dx} = \frac{x + y}{x -y}

 

 

 

 
 
 
 
 

Answers (1)

Given \log(x^2 + y^2) = 2\tan^{-1}\left (\frac{y}{x} \right ). Show that \frac{dy}{dx} = \frac{x + y}{x -y}

Differentiating both sides w.r.t x we get

\frac{1}{x^2+y^2}\left(2x +2y\frac{dy}{dx}\right) = 2\frac{1}{1+\frac{y^2}{x^2}}\times \left [ \frac{\frac{dy}{dx}x - y}{x^2}\right ]

x +y\frac{dy}{dx} = {\frac{dy}{dx}x - y}

x +y = {\frac{dy}{dx}x - y\frac{dy}{dx}}

\frac{dy}{dx} = \frac{x + y}{x-y}

Hence proved.

Posted by

Ravindra Pindel

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 Central Sector Scheme of Scholarship 2025 applications open on scholarships.gov.in
anam-khan

CBSE Board 2025: Class 10th, 12th supplementary date sheet out; exams from July 15
anam-khan

CBSE issues final reminder to schools for supplementary exam LOC submission; submit by today without late fee

Latest Question