A curve has the equation y=sin(x)cos(x), find the gradient of this curve when x = pi. (4 marks)

Option 1 - Differentiate using product rule giving dy/dx = cos2(x) - sin2(x). (2 marks) Subbing in x as pi (1 mark) then gives (-1)+ (0). Therefore the gradient is 1 (1 mark).  Option 2 - Initially changing sin(x)cos(x) into (sin2x)/2 (1 mark) using double angle identities, then using the chain rule to differentiate to cos(2x) (2 marks), finally subbing in x = pi for the answer of 1 (1 mark).

MD
Answered by Mark D. Maths tutor

5926 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Let p(x) =30x^3 - 7x^2 -7x + 2. Prove that (2x+1) is a factor of p(x).


Integrate y=x^2 between the limits x=3 and x=1


How do you integrate y = 4x^3 - 5/x^2?


I am struggling understanding how to differentiate negative indices. I get confused with the power increasing or decreasing.


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