Differentiate y=ln(ln(x)) with respect to x.

To solve this question we need to understand the process of implicit differentiation, which is a case of using the chain rule. If you remember the chain rule states that for y=f(g(x)), we have y'=f'(g(x))g'(x), so that we treat y as being composed of two functions and differentiate them individually, then multiply. So instead if we have f(y)=g(x), then using the same rule on the left hand side but with y, and differentiating both sides we get y'f'(y)=g'(x). Now that this is understood we can solve the question. We are given y=ln(ln(x)) so ey = ln(x). Now differentiate this on both sides: y'ey=1/x. Now we're looking for y' on one side and everything else on the other:y'=1/(xey). We're almost there but there's a problem, we want y' with respect to x so we need the right hand side only with x: fortunately we know ey=lnx, so y'=1/(xln(x)). And we are done. Can you differentiate y = ln(ln(x2)) for me?

Answered by Marek K. Maths tutor

4486 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I find the equation of the tangent of a curve at a specific point.


two balls of similar size masses m and 2m are moving at speeds u and 2u along a frictionless plane, they collide head on and are reflected, assuming that the coefficient of restitution of this collision is 1, what the speeds are afterwards in u


Differentiate with respect to x, x^2*e^(tan(x))


What is a logarithm?


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