Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.5 question 17 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.5 question 17 maths textbook solution

Answers (1)

Answer: \frac{d y}{d x}=\left[\frac{\tan ^{-1} x}{x}+\frac{\log x}{1+x^{2}}\right] \cdot \tan ^{-1} x

Hint: Diff by x^{\tan ^{-1} x}

Given: x^{\tan ^{-1} x}

Solution:  Let y=x^{\tan ^{-1} x}

Taking log on both sides

        \begin{aligned} &\log y=\log x^{\tan ^{-1} x} \\\\ &\frac{1}{y} \frac{d y}{d x}=\tan ^{-1} x \cdot \frac{1}{x}+\log x \cdot \frac{1}{1+x^{2}} \end{aligned}

        \frac{1}{y} \frac{d y}{d x}=\frac{\tan ^{-1} x}{x}+\frac{\log x}{1+x^{2}}

        \begin{aligned} &\frac{d y}{d x}=\left(\frac{\tan ^{-1} x}{x}+\frac{\log x}{1+x^{2}}\right) y \\\\ &\frac{d y}{d x}=x^{\tan ^{-1} x}\left[\frac{\tan ^{-1} x}{x}+\frac{\log x}{1+x^{2}}\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 Class 12 Physics paper well-balanced, moderate in difficulty; MCQ lengthy, calculation-based
anam-khan

CBSE Board 2026 Exam LIVE: Class 12 physics 'moderate' in difficulty; set-wise answer key updates
anam-khan

Less bias, more risk? CBSE on-screen marking system leaves Class 12 students, teachers cautious but optimistic

Latest Question