Differentiate the function f(x) = 3x^2/sin(2x)

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6xsin(2x). uv' = 6x^2cos(2x), v^2 = 4cos^2(2x) Therefore the differential is [6xsin(2x) - 6x^2cos(2x)]/[4cos^2(2x)] We can factor out 6x from the top and divide by the 4 on the bottom to give 3x(sin(2x)-xcos(2x))/(2*cos^2(2x))

Answered by Kilian S. Maths tutor

5375 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The equation 2x^2 + 2kx + (k + 2) = 0, where k is a constant, has two distinct real roots. Show that k satisfies k^2 – 2k – 4 > 0


express 9^(3x+1) in the form 3^(ax+b)


Does the equation: x^2+5x-6 have two real roots? If so what are they?


Differentiate 5x^2+5y^2-6xy=13 to find dy/dx


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