Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Differentiate the functions w.r.t. x. log x^cos x

 Q3  Differentiate the functions w.r.t. x.   (\log x ) ^{\cos x}

 

Answers (1)

best_answer

Given function is
y=(\log x ) ^{\cos x}
take log on both the sides
\log y=\cos x\log (\log x )
Now, differentiation w.r.t x is
\frac{d(\log y)}{dx} = \frac{d(\cos x\log(\log x))}{dx}\\ \frac{1}{y}.\frac{dy}{dx} = (-\sin x)(\log(\log x)) + \cos x.\frac{1}{\log x}.\frac{1}{x}\\ \frac{dy}{dx}= y( \cos x.\frac{1}{\log x}.\frac{1}{x}-\sin x\log(\log x) )\\ \frac{dy}{dx} = (\log x)^{\cos x}( \frac{\cos x}{x\log x}-\sin x\log(\log x) )
Therefore, the answer is  (\log x)^{\cos x}( \frac{\cos x}{x\log x}-\sin x\log(\log x) )
 

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 Class 12 West Asia special exam date sheet 2026 out; admit cards from October 12
anam-khan

CBSE Class 10, 12 private exams 2026-27 registration begins on cbse.gov.in, check eligibility and fees
anam-khan

CBSE Date Sheet 2027 LIVE: Form filling for Class 10, 12 private students closes on Oct 23; exam dates soon

Latest Question