CALCULUS Understanding
Its Concepts and Methods
CALCULUS Understanding
Its Concepts and Methods
Rules for derivatives
Rules for derivatives
Sum rule:The derivative of the sum or difference of two functions is the sum or difference of their derivatives. (u + v)' = u' + v'
Constant multiple:The derivative of a constant times a function is the constant times the derivative of the function. (ku)' = ku'
Constant
function:The
derivative of a constant function is
zero.
Power
rule:The
derivative of
xn
is
nxn-1.
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'
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.
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).
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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.