Differentiate y=x^2cos(x)

This is done using the product rule: dy/dx=udv/dx +vdu/dxset y=uv therefore u=x^2 v=cos(x)differentiate these with respect to x du/dx= 2x as you multiply by the power and then subtract the power by 1dv/dx= -sin(x) these are one the derivatives that have to be learnt for the examplug these values into the product rule to get the following:dy/dx= (x^2)(-sin(x)) + (cos(x))(2x)rewritten to dy/dx= 2xcos(x) - x^2sin(x)can be further simplified by factorising and taking out the x to get the final answer: dy/dx = x(2cos(x) - xsin(x))

Answered by Kavita K. Maths tutor

2446 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Given y = 3x^(1/2) - 6x + 4, x > 0. 1) Find the integral of y with respect to x, simplifying each term. 2) Differentiate the equation for y with respect to x.


Solve the equation 2log (base 3)(x) - log (base 3)(x+4) = 2


Calculate the derivative of the following function: f(x)=cos(3x))^2


Solve for x, between 0 and 360 degrees, 4cos2 (x) + 7sin (x) – 2 = 0


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences