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^ (−3). So (using the definition) dy/dx=(3+16t^ (−3)) X ( 1/3(t-1)^2) = (3 + 16𝑡^−3)/(3(𝑡 − 1)^ 2). 

Answered by Adil F. Maths tutor

3080 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y=(x^2+1)(e^-x)


how do integrate an equation with a surd or a fraction?


integration by parts: x^-2lnx


(The question is too long so it's marked at the top of the answer space, sorry for any inconveniences)


We're here to help

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