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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) = `d/(dx) ((x - a)/(x - b))`
By quotient rule,
`f'(x) = ((x - a)d/dx(x - b) - (x - a) d/dx (x - b))/(x - b)^2`
= `(1.(x - b) - (x - a) xx 1)/(x - b)^2`
= `(x - b - x + a)/(x - b)^2`
= `(a - b)/(x - b)^2`
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