Answers>Maths>IB>Article

How do you perform implicit differentiation?

Implicit differentiation is used when the function you need to differentiate is not in the form y = f(x). For example: y4 + 3x2 - 10 + 2y2 = 4xThe first step is to differentiate each term of the equation with respect to x, using the above example:(d/dx)(y4) + (d/dx)(3x2) - (d/dx)(10) + (d/dx)(2y2) = (d/dx)(4x)You can then differentiate terms only involving x as normal. To differentiate a function of y with respect to x the chain rule must be applied. Using the example, this gives:(d/dy)(y4)(dy/dx) + 6x + (d/dy)(2y2)(dy/dx) = 4You can now differentiate the terms containing y with respect to y as normal:4y3(dy/dx) + 6x + 4y(dy/dx) = 4Now factor out (dy/dx):(dy/dx)(4y3 + 4y) = 4 - 6xDivide through to get the final answer:(dy/dx) = (4 - 6x) / (4y3 + 4y)

Answered by Toby F. Maths tutor

1175 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

What is the simples way to integrate by part?


a) Let u=(2,3,-1) and w=(3,-1,p). Given that u is perpendicular to w, find the value of p. b)Let v=(1,q,5). Given that modulus v = sqrt(42), find the possible values of q.


Find the cube roots of i in the form a+bi, where a, b are real numbers.


Differentiate, from first principles, y=x^2


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