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 18 sub question (viii) maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.5 question 18 sub question (viii) maths textbook solution

 

Answers (1)

best_answer

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

Hint: Diff by x^{n-3}

Given: y=x^{x^{2}-3}+(x-3)^{x^{2}}

Solution:  y=u+v

u=x^{x^{2}-3}

\begin{aligned} &\log u=\log x^{x^{2}-3} \\\\ &\log u=\left(x^{2}-3\right) \log x \end{aligned}

\frac{1}{u} \frac{d u}{d x}=\left(x^{2}-3\right) \cdot \frac{1}{x}+\log x(2 x)

\frac{d u}{d x}=\left(\frac{x^{2}-3}{x}+2 x \log x\right) \cdot x^{x^{2}-3}

Now v=(x-3)^{x^{2}}

Take log on both sides

        \begin{aligned} &\log v=\log (x-3)^{x^{2}} \\\\ &\frac{1}{v} \frac{d v}{d x}=x^{2} \log (x-3) \end{aligned}

        \frac{d v}{d x}=\left[\frac{x^{2}}{x-3}+2 x \log (x-3)\right](x-3)^{x^{2}}

        \frac{d y}{d x}=\frac{d u}{d x}+\frac{d v}{d x}

        \left(\frac{x^{2}-3}{x}+2 x \log x\right) x^{x^{2}-3}+\left(\frac{x^{2}}{x-3}+2 x \log (x-3)\right)(x-3)^{x^{2}}

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 Results 2024: Marks verification from 4th day of result declaration; board issues schedule
anam-khan

CBSE 10th, 12th results 2024 ‘shortly’; board issues Digilocker access code for students
anam-khan

CBSE Class 10, 12 results 2024 likely after May 20, says result portal

Latest Question