Unformatted text preview: ‘ Introduction to Derivatives
Techniques of Differentiation: Basic Rules Because the derivative is a limit, many of the rules of limits apply to the
derivative: 1. (cf(x))' = c(f'(x)) where c is a constant. This says that the derivative of a
scalar multiple of a function is equal to the derivative of the function multiplied by the scalar multiple.
2. (f (x) + g(x)) = f'(x) + g'(x). The derivative of a sum of two functions is equal to the sum of the individual derivatives. The Power Rule
This is a powerful way of finding the derivative of a polynomial function. It says: ii
g(xn)=nxnl where n is a real number. For example, i
ii: (x4) =4x3 The Product Rule If f and g are two differentiable functions, then (fg)' = f’g + g’f. For example, {I 1
ﬁ((3x)(ﬁl = 3x5 +3X(§x‘i) The Quotient Rule If f and g are two differentiable functions, then (i)’_ 5:11—45 9 9 For example, ( 3: )’ (2+1)(3)—l1)(3:r) 3
1+1 (2+1? =(2+1? ...
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 Spring '10
 DrCarlDillion

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