given y = x^2 - 7x + 5, find dy/dx from first principles

using the delta method for first principles derivation:
Define the differential: dy/dx = limit as h -> 0 f(x+h) - f(x)/h where f(x) = ysubstitute the equation into the differential: dy/dx = (x+h)^2 - 7*(x+h) + 5 - (x^2 - 7x +5)/hexpand the brackets to form quadratic: dy/dx = x^2 + h^2 + 2xh - 7x -7h + 5 - x^2 + 7x - 5/hcancel out the variables: dy/dx = h^2 + 2xh - 7h / hdivide by h: dy/dx = h + 2x - 7Finish it off by taking the limit of h to be 0: dy/dx = 2x - 7 Simple method to follow with an example for a 5 mark question that consistently comes up in core 1.

Answered by Dafydd B. Maths tutor

7256 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

differentiate 2^x


The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.


Why does differentiation give us the results that it does?


How do you find the minimum of the equation sin^2(x) + 4sin(x)?


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