The function f is defined for x > 0 by f (x) = x^1n x. Obtain an expression for f ′ (x).

By taking the natural log on both sides we can see that: ln(f(x)) = ln(x)^2 This is a more familiar expression that we know how to differentiate  LHS: f '(x)/f(x), RHS: 2*ln(x)/x By rearranging this we can see that  f '(x) = f(x)2ln(x)/x Substituting our original f(x) expression back into this we find that: f '(x) = x^ln(x)2ln(x)/x = x^(ln(x)-1)2ln(x).

SE
Answered by Steven E. Further Mathematics tutor

2453 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Prove e^(ix) = cos (x) + isin(x)


Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).


How do I determine whether a system of 3 linear equations is consistent or not?


Differentiate artanh(x) with respect to x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences