Differentiate with respect to x: y = xln[2x]

This is an example of a question where we would have to use the product rule for differentiation, because we have two functions multiplied together ( x and ln(2x) ).If we have: y = uv, where u and v are functions of x then the product rule tells us that dy/dx = uv' + vu'. So, if u = x and v = ln[2x] then u' = 1 and v' = 1/x . Remember that the differential of ln(f(x)) = f'(x) / f(x)Then, applying the product rule, we have that dy/dx = (x) (1/x) + (ln(2x)) (1) = 1 + ln(2x) Our final answer is: 1 + ln(2x)

MA
Answered by Muhammed Ali M. Maths tutor

4803 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate f(x)= x^3 + x^(1/3)-2


Let C : x^2-4x+2k be a parabola, with vertex m. By taking derivatives or otherwise discuss, as k varies, the coordinates of m and, accordingly, the number of solutions of the equation x^2-4x+2k=0. Illustrate your work with graphs


How do I prove (x-2) is a factor of the function f(x) = x^2-4x+4?


Three forces of magnitude 50N, PN, QN all act in a horizontal plane in equilibrium. The diagram shows the forces. DIAGRAM: QN = EAST, 50 = SOUTH, PN = 120 DEGREES ANTICLOCKWISE FROM QN a) Find P. b) Find Q.


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