Question 3a (ii)
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Question 3 a) Differentiate the following expressions. There is no need to simplify to a single fraction. x x − x2 x+2 Suggested Solution • 1mk correct u1 • 1mk correct v1 • 1mk correct quotient/product rule Solution
d x x − x2 dx x +2
•
u = x x − x2
= x1 x =x
vu ′ − uv ′ = v2
u′ =
•
3
2
1
2
− x2
−x2
3 12 x − 2x 2
v = ( x +2)
v′ =
1
2
1 −1 ( x + 2) 2 2
d x x − x2 dx x +2
•
u = x x − x2
= x1 x =x
vu ′ − uv ′ = v2
u′ =
•
3
2
1
2
− x2
−x2
3 12 x − 2x 2
v = ( x +2)
v′ =
1
2
1 −1 ( x + 2) 2 2
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