What is the gradient of y = xcos(x) at x=0?

First we want to calculate the derivative of y. To do this we use the product rule:If we rewrite y as y = uv, then dy/dx = vdu/dx + udv/dx.Here, we have u = x and v = cos(x).That means du/dx = 1 and dv/dx = -sin(x).Therfore dy/dx = cos(x)1 + x(-sin(x)) = cos(x) - xsin(x).To evaluate the gradient of y at x=0 we substitute x=0 into the derivative we have just calculated:gradient = cos(0) - 0*sin(0) = 1

FF
Answered by Fraser F. Maths tutor

4223 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is differentiation and how is it done?


Common mistakes made in A-Level exams


Solve sec(x)^2-2*tan(x)=4 for 0<=x<=360


express the following fraction in the form of m + (n)^1/2. the fraction is ((3*(5)^1/2)^2 - 7)/(3 + 7*(5)^1/2). where m,n are real numbers.


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