How do i find dy/dx in terms of t for two parametric equations that are in terms of t.

To differentiate parametric equations we have to use the chain rule in a special way.
We know that the chain rule can be written as dy/dx = dy/dt * dt/dx, as both dts cancel. But if we have an equation x in terms of t, and an equation y in terms of t, the above equation will no longer work, as we want dy/dt, but also dx/dt (rather than dt/dx).
To manage this the trick we use is simply to rewrite the equation as dy/dx = dy/dt / dx/dt. Using this we can now differentiate both equation y and equation x like normal, then put them as a fraction with dy/dt on top and dx/dt on the bottom and reduce this fraction to its simplest form.

BW
Answered by Ben W. Maths tutor

4472 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A ball is projected vertically upwards from the ground with speed 21 ms^–1. The ball moves freely under gravity once projected. What is the greatest height reached by the ball?


Showing all your working, evaluate ∫ (21x^6 - e^2x- (1/x) +6)dx


A ball is projected at an angle b from the horizontal. With initial velocity V the ball leaves the ground at point O and hits the ground at point A. If Vcos(b) = 6u and Vsin(b) = 2.5u, how long does the ball take to travel between O and A.


what is the integral of ln(x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences