Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 11

Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 11

Answers (1)

Answer:   (\log x)^{\log x}\left(\frac{1}{x}+\frac{\log (\log x)}{x}\right)

Hint: Diff by (\log x)^{\log x}

Given:(\log x)^{\log x}

Solution:  Let y=(\log x)^{\log x}

Taking log on both sides

        \begin{aligned} &\log y=\log (\log x)^{\log x} \\\\ &\log y=\log x \cdot \log (\log x) \end{aligned}                \left[\because \log \left(a^{b}\right)=b \log a\right]

Differentiate w.r.t x,

        \frac{1}{y} \frac{d y}{d x}=d \frac{(\log x \cdot \log (\log x)}{d x}

Use product rule

        \begin{aligned} &(u v)^{\prime}=u^{\prime} v+v^{\prime} u \\\\ &\frac{1}{y} \frac{d y}{d x}=\frac{d(\log x)}{d x} \cdot \log (\log x)+d \frac{(\log (\log x)}{d x} \cdot \log x \end{aligned}

        \begin{aligned} &\frac{1}{y} \frac{d y}{d x}=\frac{1}{x} \log (\log x)+\frac{1}{\log x}+\frac{d(\log x)}{d x} \log x \\\\ &\frac{1}{y} \frac{d y}{d x}=\frac{1}{x} \log (\log x)+\frac{d(\log x)}{d x} \end{aligned}

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

 

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 2026 Admit Card LIVE: CBSE Class 10, 12 hall ticket soon at cbse.gov.in; direct link, datesheet, updates
anam-khan

CBSE 2026 Admit Card LIVE: CBSE Class 10, 12 hall tickets for private candidates declared at cbse.gov.in
anam-khan

Looking forward to interacting with students at Pariksha Pe Charcha 2026: PM Narendra Modi

Latest Question