Find the derivative (dy/dx) of the curve equation x^2 -y^2 +y = 1.

Most of the differentiation problems require us to apply one of the well known rules, be it product rule, quotient rule or chain rule. But those problems have one thing in common:  explicite formula for y, be it y = ln(x) or y = sin(x)/(x2 + 1).

In our example it's too difficult to isolate y, hence we will have to use implicit differentiation e.g. we will have to differentiate each term of the equation with respect to x.  Differentiating  (d/dx) yields,

d/dx [x2]  -   d/dx [y2] + d/dx [y] = d/dx [1]  =>

2x - 2y (dy/dx) + (dy/dx) = 0 =>

(dy/dx) (2y -1) =  2x   =>     (dy/dx) = 2x/(2y-1)

In our solution, we used the fact that the derivative of ywith respect to x is equal to 2y(dy/dx).

Answered by Adam G. Maths tutor

4329 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the integral of [ 2x^4 - (4/sqrt(x) ) + 3 ], giving each term in its simplest form


Differentiate y = x^3− 5x^2 + 3x


The complex numbers Z and W are given by Z=3+3i and W=6-i. Giving your answers in the form of x+yi and showing how you clearly obtain them, find: i) 3Z-4W ii) Z*/W


What is the centre and radius of the circle x^2+y^2-6x+4y=-4


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