Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Differentiate w.r.t. x the function in Exercises 1 to 11. log x ^ log x

 Q7  Differentiate w.r.t. x the function in Exercises 1 to 11. ( \log x )^{ \log x } , x > 1

Answers (1)

best_answer

Given function is
y=( \log x )^{ \log x } , x > 1
Take log on both sides 
\log y=\log x\log( \log x )
Now, differentiate w.r.t.
\frac{1}{y}.\frac{dy}{dx}= \frac{1}{x}.\log (\log x)+\log x.\frac{1}{\log x}.\frac{1}{x} = \frac{\log x+1}{x}
\frac{dy}{dx} = y.\left ( \frac{\log x+1}{x} \right )\\
\frac{dy}{dx} = (\log x)^{\log x}.\left ( \frac{\log x+1}{x} \right )\\
Therefore, differentiation w.r.t x is (\log x)^{\log x}.\left ( \frac{\log x+1}{x} \right )\\

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

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
anam-khan

CBSE Exam Dates 2026 LIVE: CBSE Class 10th, 12th revised date sheet at cbse.gov.in; how to download, updates

Latest Question