How do I implicitly differentiate and why does it work? (Assuming understanding of differentiation)

Implicit differentiation can be used when you are asked to find dy/dx of a function that has not been written as y=f(x) e.g. y = x^2 - 1, and which cannot be rearranged as such. We can use the equation of a circle as an example, x^2 +y^2 = 25. In order to implicitly differentiate we have to differentiate each term with respect to x, this is straight forward for the x^2 and 25 terms but for any term which is a function of y we differentiate pretending that y is just another x term and then multiply that by dy/dx. e.g. y^2 -> 2ydy/dx. Once all the terms have been dealt with we can rearrange to find dy/dx.Why does this work? Let's consider what differentiating a function of y with respect to y looks like: df(y)/dy, but we need to find df(y)/dx so if we times df(y)/dy x dy/dx we can see that the product is now df(y)/dx for that term.

SO
Answered by Sorcha O. Maths tutor

3410 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Can you help me understand how Arithmetic sequences work?


Express x^2 + 5x + 10 in the form (x+p)^2 +q


Find the equation of the line through the following points: (-2, -3) and (1, 5)


How do you integrate sin^2(3x)cos^3(3x) dx?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning