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If f(x)=2x+43x+7 f(x) = \frac{2x + 4}{3x + 7} f(x)=3x+72x+4, what is the value of f′(3)f'(3)f′(3)?
If f(x)=−9xx2+5f(x)=\frac{-9x}{x^2+5} f(x)=x2+5−9x, what is the value of f′(5)f'(5)f′(5)?
Let g(x)g(x)g(x) be a differentiable function such that g(0)=2.g(0)=2.g(0)=2. If f(x)=1xg(x)+6,\displaystyle f(x)=\frac{1}{xg(x)+6},f(x)=xg(x)+61, where what is the value of f′(0)?f'(0)?f′(0)?
Let g(x)g(x)g(x) be a differentiable function such that g(x)≠−7.g(x) \neq -7.g(x)=−7. If f(x)=x7+g(x)f(x)=\frac{x}{7+g(x)}f(x)=7+g(x)x and f′(0)=114,f'(0)=\frac{1}{14},f′(0)=141, what is the value of g(0)?g(0)?g(0)?
If aaa and bbb are constants such that f(x)=ax+bx2+x+1f(x)=\frac{ax+b}{x^2+x+1}f(x)=x2+x+1ax+b and f′(0)=−3, f′(−1)=10,f'(0)=-3, \; f'(-1)=10,f′(0)=−3,f′(−1)=10, what is 2a+b?2a+b?2a+b?
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