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))

KS
Answered by Kilian S. Maths tutor

5632 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate x^x


Given that 2cos(x+50)°=sin(x+40)° show tan x° = tan 40°/3


Express x^2-7x+2 in the form (x-p)^2+q where p and q are rational. Hence or otherwise find the minimum value of x^2-7x+2


The curve C has equation 2yx^2 + 2x + 4y - cos(πy) = 45. Using implicit differentiation, find dy/dx in terms of x and y


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