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Question
Find the derivative of (5x3 + 3x – 1) (x – 1).
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Solution
Let f (x) = (5x3 + 3x – 1) (x – 1) ...(1)
Differentiating (1) with respect to x, we get
f'(x) = (5x3 + 3x - 1) (x - 1) + (5x3 + 3x - 1)(x - 1)
= f'(x) = (5.3x2 + 3 - 0) (x - 1) + (5x3 + 3x - 1) (1 - 0)
= (15x2 + 3) (x - 1) + (5x3 + 3x -1) (1)
= 15x3 + 3x - 15x2 - 3 + 5x3 + 3x - 1
∴ f'(x) = 20x3 - 15x2 + 6x - 4
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