Differentiate with respect to X: x^2 + 2y^2+ 2xy = 2

  • Google+ icon
  • LinkedIn icon
  • 605 views

Assuming the correct tools of differentiation have been taught, we can tackle each term seperately and then rearrange to have dy/dx as the subject.

Taking a look at the first term, x^2,  differentiating this term would become 2x (diffentiating x^n = nx^n-1)

Taking a look at the second term, 2y^2, it would appear we could differentiate it just like we did the first term. However this variable involves y and not x, meaning we must differentiate it implicitly.Therefore differentiating 2y^2 would become 4y(dy/dx)

Taking a look at the third term, 2xy, we immediately notice that it has both x terms and y terms involved; this should immediately hint to us that the product rule should be used. Therefore differentiating 2xy would become 2y + 2x(dy/dx) (Differentiating any term involving any other variable other than x with respect to x would require implicit differentiation).

Differentiating any constant (2) would = 0

Putting all these terms together would give:

2x + 4y(dy/dx) + 2y + 2x(dy/dx) = 0

With our basic GCSE knowledge of subject formula we can get:

2x + (dy/dx)(4y+2x) = 0

dy/dx = (-2x) / (4y+2x)

Callum O. GCSE Maths tutor, A Level Maths tutor, 11 Plus Maths tutor,...

About the author

is an online A Level Maths tutor with MyTutor studying at Warwick University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

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

mtw:mercury1:status:ok