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Question
For some constants a and b, find the derivative of (x – a) (x – b).
Solution
Let f (x) = (x – a) (x – b)
f(x) = x2 – (a + b)x + ab
∴ f'(x) = `d/(dx) (x^2 - (a + b)x + ab)`
= `d/(dx) (x^2) - (a + b) d/(dx) (x) + d/(dx) (ab)`
Using the theorem `d/(dx) (x^n) = nx^(n - 1)`, we obtain
f'(x) = 2x - (a + b) + 0
= 2x - a - b
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