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If $f(x) = \frac{2x + 4}{3x + 7}$, what is the value of $f'(3)$?

If $f(x)=\frac{-9x}{x^2+5}$, what is the value of $f'(5)$?

Let $g(x)$ be a differentiable function such that $g(0)=2.$ If $\displaystyle f(x)=\frac{1}{xg(x)+6},$ where what is the value of $f'(0)?$

Let $g(x)$ be a differentiable function such that $g(x) \neq -7.$ If $f(x)=\frac{x}{7+g(x)}$ and $f'(0)=\frac{1}{14},$ what is the value of $g(0)?$

If $a$ and $b$ are constants such that $f(x)=\frac{ax+b}{x^2+x+1}$ and $f'(0)=-3, \; f'(-1)=10,$ what is $2a+b?$

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