How do I do implicit differentiation?

The main thing to remember with implicit differentiation is to differentiate each thing as you see it. Don't worry about rearranging the equation until you have differentiated everything first. Say you have the question,

Differentiate x^2 + y^2 = 1 with respect to x.

Starting from the left, the differential of x^2 with respect to x is 2x. 

Next we have y^2. When we have a term that is not what we are differentiating with respect to (ie y is not x) then you differentiate the term as you would do normally but you have to put a dy/dx on the end. So the differential of y^2 with respect to x is 2y(dy/dx).

And of course the differential of 1 with respect to 1 is 0 (as is the case with any constant.)

This leaves us with a result of:

2x + 2y(dy/dx) = 0

Often this can be your final answer but if you are asked to make dy/dx the subject then you just rearrange the equation to make this the case.

If you do this correctly, you will find your answer to be dy/dx = - (x/y)

Thomas H. A Level Maths tutor, IB Maths tutor, 13 plus  Maths tutor, ...

11 months ago

Answered by Thomas, who has applied to tutor A Level Maths with MyTutor

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


£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£30 /hr

Anuradha D.

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 4 more

Further Mathematics
-Personal Statements-

“Hello everyone! My name is Anuradha (you can call me Anu), and I am a Physics Undergrad at Durham. I have always had a “thing” for science and am so pleased to be studying it – and hope that I can give you all the support you need to ...”

£20 /hr

Shivani M.

Degree: Medicine (Bachelors) - Exeter University

Subjects offered:Maths, Chemistry+ 4 more

.BMAT (BioMedical Admissions)
-Medical School Preparation-

“I graduated with 5 A-levels last year and now study medicine at Exeter. I have mentored GCSE maths students for the last 2 years. I would love to hear from you!”

About the author

£20 /hr

Thomas H.

Degree: MSci Mathematics and Philosophy (Masters) - Bristol University

Subjects offered:Maths


“About Me Hi! I'm a Maths and Philosophy student at the Univeristy of Bristol and I'd like to help you with your maths!  I have experience working with children of all ages, from little kids just learning the fundamentals, all the way...”

MyTutor guarantee

You may also like...

Posts by Thomas

How do I divide fractions?

How do I do implicit differentiation?

How do I write a number as a product of its prime factors?

Other A Level Maths questions

What is the chain rule? when do I have to use it?

Evaluate the indefinite integral: ∫ (e^x)sin(x) dx

Use the chain rule to differentiate y=1/x^2-2x-1

Find dy/dx when y = x^2(cos(x)).

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