How do i use chain rule to calculate the derivative dy/dx of a curve given by 2 "parametric equations": x=(t-1)^3, y=3t-8/t^2

(Explain why it is called "parametric"). The definition of chain rule says that we can re-write the derivative dy/dx in terms of the "parameter t" by dy/dx = (dy/dt) X (dt/dx). (Explain why this is the case).
So we have two equations, x and y, both equal to some perimeter t. To calculate the derivative dy/dx is simply the same as calculating the derivatives w.r.t "t" (either by inspection, product, or quotient rules) and then we multiply them together using the definition. That is dx/dt = 3(t-1)^2 , dy/dt = 3+16t^ (βˆ’3). So (using the definition) dy/dx=(3+16t^ (βˆ’3)) X ( 1/3(t-1)^2) = (3 + 16𝑑^βˆ’3)/(3(𝑑 βˆ’ 1)^ 2).Β 

AF
Answered by Adil F. β€’ Maths tutor

3535 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers β–Έ

Can you explain the sum of 1 to 100?


find x: e^(3x-9) = 8


Why does 1/x integrate to lnx?


Given that y=(4x+1)^3sin 2x , find dy/dx .


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

Β© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences