MYTUTOR SUBJECT ANSWERS

76 views

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...

3 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

183 SUBJECT SPECIALISTS

£20 /hr

Chloe H.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered: Maths

Maths

“Hi there! My name is Chloe, I'm doing maths at the University of Warwick.  I love maths and I have a passion for helping other people understand it. I have previously tutored GCSE students as well as students in lower years. I am frie...”

MyTutor guarantee

£22 /hr

Bryan P.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I am currently a BSc Mathematics student at the University of Bristol and I am already no stranger to teaching.I have worked as a teaching assistant in my secondary school's maths department where I also led one-on-one sessions with ...”

£20 /hr

Matthew M.

Degree: Engineering Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Law+ 1 more

Maths
Law
History

“I am an Engineering Math student at the University of Bristol. I have a range of interests, which cover maths, history and law, and would love to help others in these areas as well as encourage the same enthusiasm I have in others! I a...”

MyTutor guarantee

About the author

£20 /hr

Seb G.

Degree: Mathematics (Masters) - Bath University

Subjects offered: Maths

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

Find the stationary point of y=3x^2-12x+29 and classify it as a maximum/minimum

Find the equation of the normal line at the point H, where θ= π/6, on the curve with equations x=3sinθ and y=5cosθ

Differentiate a^x with respect to x

Express (2x-1)/(x-1)(2x-3) in partial fractions.

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok