<s>[INST] Difference in derivative between $\frac{6}{3x^2+1}$ and $\frac{6}{3x^2}$ Is there a difference in derivative between $\frac{6}{3x^2+1}$ and $\frac{6}{3x^2}$ I thought there wouldn't be and I've asked several people all with different results?
 [/INST] Let $$f(x) = \frac{6}{3x^2+1}$$
Then we have 
$$\tag{1}f'(x) = \frac{d/dx(6)\cdot(3x^2+1)-6\cdot d/dx(3x^2+1)}{(3x^2+1)^2} = \frac{-6\cdot6x}{(3x^2+1)^2}$$
Since $\frac{d}{dx} ~3x^2+1 = \frac{d}{dx}~ 3x^2$ there is no difference upstairs in $(1)$, but only in the denominator. 
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