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

5405 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate y=x^2 between the limits x=3 and x=1


The mass, m grams, of a substance is increasing exponentially so that the mass at time t hours is m=250e^(0.021t). Find the time taken for the mass to double in value.


Integral of sin^2(x) with respect to x


Solve the following simultaneous equations y + 4x + 1 = 0, y^2 + 5x^2 + 2x = 0


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