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Question
(2x – 7)2 (3x + 5)3
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Solution
`d/(dx) (2x - 7)^2 (3x + 5)^3`
= `(2x - 7)^2 * d/(dx) (3x + 5)^3 + (3x + 5)^3 * d/(dx) (2x - 7)^2`
= `(2x - 7)^2 * 3(3x + 5)^2 * 3 + (3x + 5)^3 * 2(2x - 7) * 2` .....[Using product rule]
= `9(2x - 7)^2 (3x + 5)^2 + 4(3x + 5)^3 (2x - 7)`
= `(2x - 7) (3x + 5)^2 [9(2x - 7) + 4(3x + 5)]`
= `(2x - 7) (3x + 5)^2 (18x - 63 + 12x + 20)`
= `(2x - 7)(3x + 5)^2 (30x - 43)`
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