Calculus

Differentiation Rules

Differentiation - Quotient Rule

         

If f(x)=2x+43x+7 f(x) = \frac{2x + 4}{3x + 7} , what is the value of f(3)f'(3)?

If f(x)=9xx2+5f(x)=\frac{-9x}{x^2+5} , what is the value of f(5)f'(5)?

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

Let g(x)g(x) be a differentiable function such that g(x)7.g(x) \neq -7. If f(x)=x7+g(x)f(x)=\frac{x}{7+g(x)} and f(0)=114,f'(0)=\frac{1}{14}, what is the value of g(0)?g(0)?

If aa and bb are constants such that f(x)=ax+bx2+x+1f(x)=\frac{ax+b}{x^2+x+1} and f(0)=3,  f(1)=10,f'(0)=-3, \; f'(-1)=10, what is 2a+b?2a+b?

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