Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 39

Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 39

Answers (1)

Answer:

Proved

Hint:

You must know the derivative of sin and logarithm function

Given:

y=\sin (\log x) , \text { prove } x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0

Solution:

y=\sin (\log x)

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

        \begin{aligned} &\text { Now, }\\ &\text { LHS }=x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y\\ &=\frac{x^{2}\{-\cos (\log x)-\sin (\log x)\}}{x^{2}}+\frac{x \cos (\log x)}{x}+\sin (\log x)\\ &=0=\mathrm{RHS} \end{aligned}

Posted by

Gurleen Kaur

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 cuts re-evaluation fee to Rs 100; defends OSM
anam-khan

CBSE defends OSM evaluation process, says re-evaluation option remains open
anam-khan

‘Feeling Devastated’: CBSE 12th students allege low marks due to on-screen marking; call for manual evaluation

Latest Question