Page 106 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, University Preparation
algebraically the chain rule using monomial functions [e.g., by determining the same
1
derivative for f(x) = (5x3)3 by using the chain
rule and by differentiating the simplified
1
form, f(x) = 5 3 x] and the product rule using
polynomial functions [e.g., by determining the same derivative for f(x) = (3x + 2)(2x2 – 1) by using the product rule and by differentiating the expanded form f(x) = 6x3 + 4x2 – 3x – 2]
Sample problem: Verify the chain rule by using the product rule to look for patterns in
222 thederivativesoff(x)=x +1,f(x)=(x +1), 23 24
f(x)=(x +1),andf(x)=(x +1).
3.5 solve problems, using the product and chain rules, involving the derivatives of polynomial functions, sinusoidal functions, exponential functions, rational functions [e.g., by
expressing f(x) = x2 + 1 as the product
x–1
f(x) = (x2 + 1)(x – 1)–1], radical functions [e.g.,
by expressing f(x) = √x2 + 5 as the power
1
f(x) = (x2 + 5)2 ], and other simple combinations of functions [e.g., f(x) = x sin x, f(x) = sin x ]* cos x
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
*The emphasis of this expectation is on the application of the derivative rules and not on the simplification of resulting complex algebraic expressions.
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