f(x) = sinx. Using differentiation from first principles find the exact value of f' (π/6).

The derivative of the function where x=π/6 is defined asThe limit as h->0 of [sin(h+π/6)-sin(π/6)]/hUsing the double angle formula, sin(h+π/6) = sin(h)cos(π/6) + cos(h)sin(π/6) = √3sin(h)/2 + cos(h)sin(π/6)The limit becomes [sin(h)/2 + cos(h)sin(π/6)-sin(π/6)]/hThe limit can be broken up into two partslim as h->0 of [cos(h)sin(π/6)-sin(π/6)]/h = 0 (could use l'Hospital's rule or half angle formula)lim as h->0 of [√3sin(h)/2]/h = 1/2 (small angle approximation)0+√3/2=√3/2

Related Maths A Level answers

All answers ▸

Given the equation 3x^2 + 4xy - y^2 + 12 = 0. Solve for dy/dx in terms of x and y.


Find the equation of the normal line at the point H, where θ= π/6, on the curve with equations x=3sinθ and y=5cosθ


Show how you can rewrite (x+1)(x-2)(x+3) into the form of ax^3 + bx^2 + cx + d


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


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