Why is the derivative of x^n, nx^(n-1)?

From the definition of a derivative: f'(x) = lim h->0 ((f(x+h) - f(x)) / h) Let f(x) = x^n --> d\dx x^n = lim h->0 (((x+h)^n - x^n) / h) By binomial expansion, (x+h)^n = x^n + nhx^(n-1) + n(n-1)h^2 x^(n-2) + ... + h^n --> d\dx x^n = lim h->0 ((x^n + nhx^(n-1) + n(n-1)h^2 x^(n-2) + ... + h^n - x^n) / h) = lim h->0 (nx^(n-1) + n(n-1)h x^(n-2) + ... + h^(n-1)) = nx^(n-1)

JF
Answered by Joshua F. Maths tutor

3902 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.


differentiate y=(3x)/(x^2+6)


Given that y = (sin(6x))(sec(2x) ), find dy/dx


Find the factors of x^3−7x−6


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