Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 38

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 38

Answers (1)

Answer:  \frac{d y}{d x}=\frac{x(1+\log (x+y)-y x \log y}{y \log x+x-y(1+\log x+y)}

Hint:  To solve this we add log on both sides

Given:   x^{y}+y^{x}=(x+y)^{x+y}

Solution:  

Taking log on both sides,

        \begin{aligned} &\log x^{y}+\log y^{x}=\log (x+y)^{x+y} \\\\ &y \log x+x \log y=(x+y)+\log (x+y) \end{aligned}                \left[\because \frac{d}{d x}(u-v)=u . d v+v \cdot d u\right]

        y \cdot \log x+x \log y^{\prime}+\frac{x}{y} y^{\prime}+\log y=\frac{(x+y)}{(x+y)}\left(1+y^{\prime}\right)+\log (x+y)\left(1+y^{\prime}\right)

        \begin{aligned} &=\left(1+y^{\prime}\right)(1+\log (x+y)) \\\\ &\frac{y}{x}+\log y+y^{\prime}\left(\log x+\frac{x}{y}\right)=1+\log (x+y)+y^{\prime}(1+\log (x+y)) \end{aligned}

        y^{\prime}\left(\log x+\frac{x}{y}-(1+\log (x+y))=1+\log (x+y)-\left(\frac{y}{x}+\log y\right)\right.

        y^{\prime}=\frac{x\left(1+\log (x+y)^{\prime-y}+x \log y\right)}{y \log x+x-y(1+\log (x+y))}

Posted by

infoexpert26

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 Economics Analysis: Students find exam moderately difficult; questions mostly application-based
anam-khan

CBSE Board Exam Analysis 2026 LIVE: Class 12 economics paper 'moderate to difficult level'; updates
anam-khan

CBSE Results 2026: Board warns teachers of legal action for sharing 'misleading' information on evaluation

Latest Question