Derivative Using Quotient and Product Rules

Question

The table below gives selected values for the twice-differentiable functions $$f$$ and $$g$$ and their derivatives at $$x = 4$$.

| $$x$$ | $$f(x)$$ | $$f'(x)$$ | $$f''(x)$$ | $$g(x)$$ | $$g'(x)$$ | $$g''(x)$$ |
|-----|--------|---------|----------|--------|---------|----------|
|  4  |   1    |    3    |   -2     |   2    |   -2    |    1     |

If $$h(x) = \displaystyle\frac{f(x) \cdot g'(x)}{g(x)}$$, what is the value of $$h'(4)$$?

Accepted Answer

$$-\displaystyle\frac{7}{2}$$

Answer

$$\displaystyle\frac{3}{2}$$

Answer

$$-\displaystyle\frac{5}{4}$$

Answer

$$\displaystyle\frac{1}{4}$$

Derivative Using Quotient and Product Rules

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