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Question
Find the derivative of `2/(x + 1) - x^2/(3x -1)`.
Solution
Let f(x) = `2/(x + 1) - x^2/(3x - 1)`
`f'(x) = d/dx (2/(x + 1)) - d/dx(x^2/(3x - 1))`
= `(|d/dx(2)|(x + 1) - 2d/dx (x + 1))/(x + 1)^2 - (|d/dx(x^2)|(3x - 1) - x^2d/dx (3x - 1))/(3x - 1)^2`
= `(0 - 2 xx 1)/(x + 1)^2 - (2x(3x - 1) - x^2 xx 3)/(3x - 1)^2`
= `(-2)/(x + 1)^2 - (6x^2 - 2x - 3x^2)/(3x - 1)^2`
= `(-2)/(x + 1)^2 - (3x^2 - 2x)/(3x - 1)^2`
= `(-2)/(x + 1)^2 - (x(3x - 2))/(3x - 1)^2`
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