Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • explain solution RD Sharma class 12 chapter Differentiation exercise 10.2 question 12 maths

explain solution RD Sharma class 12 chapter Differentiation exercise 10.2 question 12 maths

Answers (1)

Answer: \frac{-1}{x \log 3\left(\log _{8} x\right)^{2}}

Hint:  You must know the rules of solving derivative of logarithm function

Given: \log _{x} 3

Solution:

Let  y=\log _{x} 3

y=\frac{\log 3}{\log x}                            \left[\therefore \log _{a} b=\frac{\log b}{\log a}\right]

Differentiating with respect to x

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left(\frac{\log 3}{\log x}\right) \\ &\frac{d y}{d x}=\log 3 \frac{d}{d x}(\log x)^{-1} \end{aligned}                      [  using chain rule]

\begin{aligned} &\frac{d y}{d x}=\log 3 \times\left[-1(\log x)^{-2}\right] \frac{d}{d x}(\log x) \\ &\frac{d y}{d x}=\frac{-\log 3}{(\log x)^{2}} \times \frac{1}{x} \end{aligned}

\begin{aligned} &\frac{d y}{d x}=-\left(\frac{\log 3}{\log x}\right)^{2} \times \frac{1}{x} \times \frac{1}{\log 3} \\ &\frac{d y}{d x}=\frac{-1}{x \log 3\left(\log _{3} x\right)^{2}} \end{aligned}                    \left[\therefore \frac{\log b}{\log a}=\log _{a} b\right]

 

 

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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question