How do I differentiate implicitly?

The most important thing to remember when differentiating implicitly is that y is a function of x. Rewriting y as y(x) often makes it much clearer. For example, evaluate d/dx (y2): using the aforementioned notation, this becomes d/dx [y(x)]2. By the chain rule, it is easy to see that this is equal to dy/dx * 2y.

Perhaps an easier way of remembering this is to differentiate with respect to y, then multiply by dy/dx. For example, evaluate d/dx(ln(y)): to find the answer, we differentiate ln(y) with respect to y to get 1/y, then multiply this by dy/dx to get dy/dx * 1/y.

The above method works because of the chain rule, which states that df/dx = df/dy * dy/dx. All we are doing is renaming the function as f (in the first example f = y2, in the second example f = ln(y)) and applying this result.

Seb G. 11 Plus Maths tutor, 13 plus  Maths tutor, A Level Maths tutor...

8 months ago

Answered by Seb, an A Level Maths tutor with MyTutor

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


PremiumRyan G. GCSE Maths tutor, GCSE Physics tutor, GCSE Computing tutor, A...
£24 /hr

Ryan G.

Degree: Electrical Engineering with Renewable Energy (Masters) - Edinburgh University

Subjects offered:Maths, Physics+ 2 more

-Personal Statements-

“ I will offer a wide range of ways to learn so you can find a way that best suits you!”

Katrina M. IB Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, A ...
£20 /hr

Katrina M.

Degree: Mathematics Bsc (Bachelors) - Exeter University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics
-Personal Statements-

“Hi, I am a patient, experienced and enthusiastic tutor ready to help each student reach their full potential.”

£26 /hr

Martyna S.

Degree: Neurotechnology (Masters) - Imperial College London University

Subjects offered:Maths, Science+ 4 more

.BMAT (BioMedical Admissions)
-Personal Statements-

“PhD candidate in Bioengineering at Imperial College London. Long experience in effective tutoring!”

About the author

£20 /hr

Seb G.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths


“Me: I'm a second year maths student at the University of Bath. I fell in love with maths after a rocky start with the subject, so believe that I can help people regardless of whether they like maths or not.  I've been tutoring maths l...”

MyTutor guarantee

You may also like...

Posts by Seb

How do I differentiate implicitly?

How do I evaluate composite functions?

How do I find the prime factors of a number?

How do I multiply decimal numbers?

Other A Level Maths questions

What does dy/dx represent?

Differentiate y=x*ln(x^3-5)

Differentiate y=4x^2+3x+9

Solve dy/dx= (x√(x^2+3))/e^2y given that y=0 when x=1, giving your answer in the form y = f(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