Differentiating Big Multiple

Hi I need urgent help for this expression as I have no idea how to get its derivative:

$\displaystyle f(x)=(x^2+1)^100(x^3-7)^2(x-1)(x^{10}+x+3)^{-1}$

I have to use the ln function but I can only come up to here:

$\displaystyle \frac{d}{dx}ln(f(x))=100\frac{2x}{x^2+1}+2\frac{3x ^2}{x^3-7}+\frac{1}{x-1}-\frac{10x^9+1}{x^{10}+x+3}$

Specifically I don't know how to get rid of the natural log function on the left side of the equation. I would appreciate if anyone could tell me how?