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

4248 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Take the 2nd derivative of 2e^(2x) with respect to x.


What is the value of sin(theta), cos(theta), tan(theta) where theta = 0, 30, 45, 60, 90


Integrate the following fraction w.r.t. x: (sqrt(x^2 + 1)-sqrt(x^2 - 1))/(sqrt(x^4 - 1))


By using partial fractions, integrate the function: f(x) = (4-2x)/(2x+1)(x+1)(x+3)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning