Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 18 sub question (i)

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 18 sub question (i)

Answers (1)

Answer: x^{x} \sqrt{x}\left(\log x+1+\frac{1}{2 x}\right)

Hint:  \text { Diff by } x^{x} \sqrt{x}

Given: x^{x} \sqrt{x}

Solution:  

Let, y=x^{x} \sqrt{x}

Taking log both side  

\log y=\log x^{x} \sqrt{x} \; \; \; \; \; \; \; \; \; \; \; \quad[\log m n=\log m+\log n]

\log y=\log x^{x}+\log \sqrt{x}

\log y=x \log x+\log (x)^{\frac{1}{2}}

\log y=\left(x+\frac{1}{2}\right) \cdot \log x

\frac{d}{d x} \log y=\frac{d}{d x}\left(x+\frac{1}{2}\right) \cdot \log x

\begin{aligned} &\frac{1}{y} \frac{d y}{d x}=\frac{d}{d x}\left(x+\frac{1}{2}\right) \cdot \log x+\left(x+\frac{1}{2}\right) \cdot \frac{d}{d x} \log x \\\\ &\frac{d y}{d x}=x^{x} \sqrt{x}\left(\log x+1+\frac{1}{2 x}\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 Exam Date 2027 Highlights: Class 10, 12 exam dates soon on cbse.gov.in; private candidate form
anam-khan

CBSE 10th, 12th board exam schedule 2027: Sample papers, passing marks
anam-khan

CBSE Class 10, 12 Board Exam 2027: Schedule soon; passing marks, paper pattern

Latest Question