You should use the following substitution such that:

`y = x*f(x)`

Differentiating both sides with respect to x yields:

`(dy)/(dx) = (d(x*f(x)))/(dx)`

You need to use product rule to the right side such that:

`y' = (dy)/(dx) = f(x) + (x*d(f(x)))/(dx)`

You need to substitute `f(x) + (x*d(f(x)))/(dx)` for `y` ' and `x*f(x)` for `y` , in the given equation, such that:

`x(f(x) + (x*d(f(x)))/(dx)) =x*f(x)- xe^((x*f(x))/x)`

You...

(The entire section contains 283 words.)

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