Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Find the second order derivative if x and y are given by   and  <img alt="y=acot(t)" src="ht

Find the second order derivative if x and y are given by x=atant  and  y=acot(t)

Option: 1

\tan ^3 t


Option: 2

\sin ^3 t


Option: 3

\cot ^3 t


Option: 4

\sec ^3 t


Answers (1)

best_answer

Differentiate the functions implicitly with respect to “x”


\begin{aligned} & \frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}} \\ & \frac{d y}{d x}=-\frac{\operatorname{acosec}^2 t}{a \sec ^2 t}=-\frac{\cos ^2 t}{\sin ^2 t}=-\cot ^2 t \\ & \frac{d^2 y}{d x^2}=\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{d y}{d x}\right)=\frac{\mathrm{d}}{\mathrm{d} t}\left(-\cot ^2 t\right) \frac{d t}{d x} \\ & \frac{d^2 y}{d x^2}=-2 \cot (t) \cdot-\operatorname{cosec}^2 t \cdot \frac{1}{\sec ^2 t}=\frac{\cos ^3 t}{\sin ^3 t}=\cot ^3 t \end{aligned}

Posted by

shivangi.bhatnagar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains Result 2025 (Out) Live: NTA JEE Main session 1 scorecard at jeemain.nta.nic.in; cut-off, toppers
anam-khan

JEE Main 2025 results out for 13 lakh at jeemain.nta.nic.in; top 2.5 lakh qualify for JEE Advanced
anam-khan

JEE Main expected cut-offs 2025 for General, OBC, SC, ST, EWS; how many qualify for IIT JEE Adv?

Latest Question