The variable x=t^2 and the variable y=2t. What is dy/dx in terms of t?

This question may seem difficult but we just have to remember the rules of parametric differentiation and the chain rule.

The chain rules states that dy/dx=dy/dz*dz/dx where z is a third variable. Parametric differentiation incorporates the chain rule and states that if x=f(t) and y=g(t), where f and g are both functions of t, then dy/dx=(dy/dt)/(dx/dt).

The first step is to find dy/dt and dx/dt. If y=2t then dy/dt=2 by remembering differentiation rules and if x=t2 then dx/dt=2t. 

Now that we have dy/dt and dx/dt, the next step is to find dy/dx using the formula given in the definition. Therefore, dy/dx = 2/2t. The factor of 2 in the numerator and denominator then cancel so we are left with dy/dx=1/t. The question has asked us to leave the derivative in terms of t so we have no more steps left and we have answered the question. 

Samradnyee K. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mat...

9 months ago

Answered by Samradnyee, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Jacob F.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Maths, German+ 2 more

Further Mathematics
-Personal Statements-

“2nd year Maths undergrad with enhanced DBS (CRB) certification and experience teaching in secondary schools and at University. Fluent German speaker.”

£22 /hr

Max G.

Degree: Mathematics and Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“I am a maths and physics student at the University of Durham, for as long as I can remember i have been obsessed with all things science! I am patient, friendly and most of all understanding to the fact that the sciences aren't for ev...”

Ashika V. GCSE Maths tutor, A Level Maths tutor, IB Maths tutor, 13 P...
£26 /hr

Ashika V.

Degree: Physics (Masters) - Manchester University

Subjects offered:Maths, Physics+ 2 more

Extended Project Qualification
-Personal Statements-

“Hi I'm Ashika, a third year MPhys Physics student at the University of Manchester. I tutor in Maths and Physics, Personal Statements and the EPQ.”

About the author

£20 /hr

Samradnyee K.

Degree: Biomedical Engineering (Bachelors) - Kings, London University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“Hi, I am a Biomedical Engineering student at King’s College London. Mathematics and Physics have always been my passion and I hope to pass on my love for the subjects to you through engaging and interactive sessions specially catered ...”

MyTutor guarantee

You may also like...

Posts by Samradnyee

The variable x=t^2 and the variable y=2t. What is dy/dx in terms of t?

What is the equation of the curve that has gradient dy/dx=(4x-5) and passes through the point (3,7)?

What is the range of solutions for the inequality 2(3x+1) > 3-4x?

What is the simplest form of the fraction (8a^2+10ab)/(12a+15b)?

Other A Level Maths questions

Do the following vector equations intersect? l = (1 + μ)i + (2 - μ)j + (2μ - 5)k, and m = 2λi + 3j + (2 + λ)k.

Differentiate x^2+4x+9.

Integrate x*ln(x)

The points P (2,3.6) and Q(2.2,2.4) lie on the curve y=f(x) . Use P and Q to estimate the gradient of the curve at the point where x=2 .

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss