Quotient and Product Rule From a Table

Question

The functions $$f$$ and $$g$$ are twice-differentiable. The table below provides values for these functions and their derivatives at $$x = -2$$.

| $$x$$ | $$f(x)$$ | $$f'(x)$$ | $$f''(x)$$ | $$g(x)$$ | $$g'(x)$$ | $$g''(x)$$ |
|-----|--------|---------|----------|--------|---------|----------|
| -2  |   1    |    3    |   -1     |   2    |   -1    |    2     |

Given the function $$h(x) = \displaystyle\frac{f(x) \cdot g'(x)}{g(x) \cdot f'(x)}$$, what is the value of $$h'(-2)$$?

Accepted Answer

$$-\displaystyle\frac{11}{36}$$

Answer

$$\displaystyle\frac{7}{36}$$

Answer

$$\displaystyle\frac{1}{6}$$

Answer

$$-\displaystyle\frac{5}{36}$$

Quotient and Product Rule From a Table

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