How can I differentiate x^2+2y=y^2+4 with respect to x?

To differentiate this kind of expression you would need to use implicit differentiation. 

Although it may sound new, you already have all the skills you need to be able to do it. We will differentiate both sides of the expression. 

We will treat the x's as normal. When we encounter terms with y's in them, we will differentiate these terms and multiply each of them by 'dy/dx'. 

So, it will look like this.

Differentiating both sides, we get:

2x+2dy/dx=2ydy/dx

No, to get the derivative, we will simply rearrange the terms, solving for dy/dx:

2dy/dx-2ydy/dx=-2x

(2-2y)*dy/dx=-2x

dy/dx=-2x/(2-2y)

dy/dx=-x/(1-y)

dy/dx=1/(y-1)

Hence, our soultion is dy/dx=1/(y-1).

MS
Answered by Margarita S. Maths tutor

5673 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

write 2(sin^2(x)- cos^2(x)) + 6 sin(x) cos(x) in terms of cos(2x) and sin(2x)


What are the necessary conditions for a random variable to have a binomial distribution?


y = 4x/(x^2+5). a) Find dy/dx, writing your answer as a single fraction in its simplest form. b) Hence find the set of values of x for which dy/dx < 0


Whats the Product rule for differentiation and how does it work?


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