Differentiate 3x^(2)+xy+y^(2)=12 with respect to x

this is implicit differentiation. We start by differentiating 3x^(2) to get 6x (lower the power by 1, multiply by the original power). For xy, we use the product rule, giving us y + (x)dy/dx (this is the implicit part). y^(2) is differentiated to 2y*dy/dx, and 12 on the RHS just becomes 0. We want to get dy/dx on its own so we first collect like terms on one side, factorise, and then divide. dy/dx(x+2y)=-6x-y, hence dy/dx=-(6x+y)/(x+2y)

Answered by Noyonika L. Maths tutor

3669 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the integral of x^2 sin(x) between the limits 0 and π/2


how do you differentiate y=x^2 from first principles?


solve sin(2x)=0.5. between 0<x<2pi


"Why is Mathematics important, I wont use any of it when I start work?"


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences