`f(x) = x ln(x) - x` Differentiate the function.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to differentiate with respect to x, the given function, such that:

`f'(x) = (xln x - x)'`

`f'(x) = (xln x)' - x'`

You need to use the product rule to differentiate xln x, such that:

`(xln x)' = x'*ln x + x*(ln x)'`

`(xln x)' =1*ln x + x*(1/x)`

Reducing like terms, yields:

`(xln x)' = ln x + 1`

`f'(x) = ln x + 1 - 1`

Reducing like terms, yields:

`f'(x) = ln x`

Hence, evaluating the derivative of the function, yields `f'(x) = ln x.`