Derivative Using Quotient and Chain Rules

Question

The table below provides values for the twice-differentiable functions $$f$$ and $$g$$ and their derivatives at $$x = 5$$.

| $$x$$ | $$f(x)$$ | $$f'(x)$$ | $$f''(x)$$ | $$g(x)$$ | $$g'(x)$$ | $$g''(x)$$ |
|-----|--------|---------|----------|--------|---------|----------|
|  5  |  -1    |    2    |    3     |   3    |   -1    |    2     |

Let the function $$h$$ be defined by $$h(x) = \displaystyle\frac{[f(x)]^2}{g(x)}$$. What is the value of $$h'(5)$$?

Accepted Answer

$$-\displaystyle\frac{11}{9}$$

Answer

$$\displaystyle\frac{13}{9}$$

Answer

$$\displaystyle\frac{4}{3}$$

Answer

$$-\displaystyle\frac{4}{9}$$

Derivative Using Quotient and Chain Rules

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