 CALCULUS Understanding Its Concepts and Methods

Rules for derivatives

Rules for derivatives

1. Sum rule:The derivative of the sum or difference of two functions is the sum or difference of their derivatives. (u + v)' = u' + v'

2. Constant multiple:The derivative of a constant times a function is the constant times the derivative of the function. (ku)' = ku'

3. Constant function:The derivative of a constant function is zero. 4. Power rule:The derivative of xn is nxn-1. 5. Product rule:The derivative of a product is the first factor times the derivative of the second plus the second factor times the derivative of the first. (uv)' = uv' + vu'

6. Quotient rule:The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. 7. Chain rule:The derivative of the composition u(v(x))  is the derivative of u evaluated at v(x) multiplied by the derivative v'(x). Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.