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 10.5 question 8 maths

Explain solution RD Sharma class 12 chapter Differentiation exercise 10.5 question 8 maths

Answers (1)

Answer: e^{x \log x}(1+\log x)

Hint: Differentiate by applying e^{x}

Given: e^{x \log x}

Solution:  Let y=e^{x \log x}

        y=x^{x}                \left[\because a^{b}=e^{b \log a}\right]

Taking log on both sides

        \begin{aligned} &\log y=\log e^{x \log x} \\\\ &\log y=x \log x \end{aligned}

Differentiate w.r.t x,

        \frac{1}{y}=x \frac{d}{d x}(\log x)+\log x \frac{d}{d x} x                   [ use multiplication rule]

        \begin{aligned} &\frac{1}{y} \frac{d y}{d x}=x \cdot \frac{1}{x}+\log x .1 \\\\ &\frac{d y}{d x}=y+y \log x \end{aligned}

        \begin{aligned} &\frac{d y}{d x}=y(1+\log x) \\\\ &=e^{x \log x}(1+\log x) \end{aligned}\begin{aligned} &\frac{d y}{d x}=y(1+\log x) \end{aligned}

                =e^{x \log x}(1+\log x)

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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question