Find the derivative of a function at a certain point using the difference quotient formula - High school Calculus Exercises

Find the following derivatives using the difference quotient formula.

f : x \longmapsto \dfrac{2x^2}{1-x} for x=0

f is not differentiable for x=0.

f is differentiable for x=0 and f'\left(0\right)=0.

f is differentiable for x=0 and f'\left(0\right)=-1.

f is differentiable for x=0 and f'\left(0\right)=2.

f : x \mapsto \dfrac{2x^2 + 1}{3x^2 + 2} for x=0

f is differentiable for x = 0 and f'\left(0\right) = 0.

f is differentiable for x = 0 and f'\left(0\right) = \dfrac{1}{2}.

f is differentiable for x = 0 and f'\left(0\right) = \dfrac{1}{4}.

f is not differentiable for x = 0.

f : x \longmapsto \dfrac{x}{x^2+1} for x=1

f is differentiable for x=1 and f'\left(1\right) = 0.

f is differentiable for x = 1 and f'\left(1\right) = 0.4.

f is differentiable for x = 1 and f'\left(1\right) = 0.5.

f is not differentiable for x = 1.

f : x \mapsto 2x^2 + 2x + 6 for x=-2

f is differentiable for x = -2 and f'\left(0\right) = -6.

f is differentiable for x = -2 and f'\left(0\right) = -2.

f is differentiable for x = -2 and f'\left(0\right) = 2.

f is not differentiable for x = -2.

f : x \mapsto x^2 - 4x + 6 for x=2

f is differentiable for x = 2 and f'\left(2\right) = 0.

f is differentiable for x = 2 and f'\left(2\right) = -4.

f is differentiable for x = 2 and f'\left(2\right) = 8.

f is not differentiable for x = 2.

f : x \mapsto \dfrac{\left(x + 2\right)^2 + 3}{x - 3} for x=-3

f is differentiable for x = -3 and f'\left(-3\right) = \dfrac{2}{9}.

f is differentiable for x = -3 and f'\left(-3\right) = \dfrac{-23}{9}.

f is differentiable for x = -3 and f'\left(-3\right) = \dfrac{-2}{3}.

f is not differentiable for x = -3.

f : x \mapsto \dfrac{5-x}{10-3x^2} for x=0

f is differentiable for x = 0 and f'\left(0\right) = -0.1.

f is differentiable for x = 0 and f'\left(0\right) = -0.05.

f is differentiable for x = 0 and f'\left(0\right) = -0.5.

f is not differentiable for x = 0.