y = Sin(2x)Cos(x). Find dy/dx.

Assume base differentiation knowledge: Sin(x) = Cos(x), Cos(x) = -Sin(x)The question combines the chain and product rule. To begin, start by splitting the equation: Sin(2x)Cos(x) = Sin(2x) x Cos(x)The product rule formula is dy/dx = u(dv/dx) + v(du/dx), where in this case u = Sin(2x) and v = Cos(x).Firstly, work out du/dx: This is done using the chain rule. (The chain rule formula: y = f(g(x)), dy/dx = f'(g(x))g'(x))Use f() = Sin(), g(x) = 2x. f'() = Cos(), and g'(x) = 2. Combining these, you get Cos(2x)(2) = 2Cos(2x).dv/dx is slightly simpler as it does not involve the chain rule. Cos(x) = -Sin(x).Combining these for final values (u, v, du/dx, dv/dx) in the product rule formula gives:(Sin(2x))(-Sin(x)) + (Cos(x))(2Cos(2x)), which simplifies to 2Cos(2x)Cos(x) - Sin(2x)Sin(x).

SC
Answered by Saskya C. Maths tutor

14112 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I plot y=x^2-1?


Given two coordinate points (a1,b1) and (a2,b2), how do I find the equation of the straight line between them?


Given that sin(x)^2 + cos(x)^2 = 1, show that sec(x)^2 - tan(x)^2 = 1 (2 marks). Hence solve for x: tan(x)^2 + cos(x) = 1, x ≠ (2n + 1)π and -2π < x =< 2π(3 marks)


The curve C has equation x^2 + 2xy + 3y^2 = 4. Find dy/dx.


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