This exercise is a repeat of the Year 11 exercise on differentiation. Practice these until you are very competent at this basic skill of calculus.
1. Copy and complete the table by differentiating the given terms and expressions:
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Term
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Differentiated term
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Term
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Differentiated term
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a.
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x4
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h.
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 |
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b.
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2x6
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i.
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 |
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c.
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x21
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j.
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(2x − 3)2
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d.
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5x5
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k.
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3x(2x − 6)
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e.
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3x2 + 3x
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l.
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(x + 3)(x − 5)
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f.
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2x2 + 5x + 6
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m.
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4(x − 2)2
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g.
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2(x − 4)
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n.
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x2(x2 − 2x − 9)
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2. Differentiate each of the following polynomial functions. Use appropriate notation.
a. f(x) = 4x3 − 5x2 + 8x − 12
b. y = 5x10 − 6x5 + 3x
c. g(x) = (x + 2)(x − 7)
d. y = x(x − 6)(x + 4)
3. Copy and complete the table by differentiating the given terms and expressions:
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Term
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Differentiated term
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Term
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Differentiated term
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a.
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x-3
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f.
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 |
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b.
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g.
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c.
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h.
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d.
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i.
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e.
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j.
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4. Differentiate each of the following functions. Use appropriate notation.
a. 
b. 
c. 
d. 
