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.

SG
Answered by Seb G. Maths tutor

4393 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find dy/dx of 5x^2 + 2y^3 +8 =17.


Find the x co-ordinates of the stationary points of the graph with equation y = cos(x)7e^(x). Give your answer in the form x = a +/- bn where a/b are numbers to be found, and n is the set of integers.


Differentiate with respect to x: 3 sin^2 x + sec 2x


The curve C has the equation y = 2x^2 -11x + 13. Find the equation of the tangent to C at the point P (2, -1).


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