What is f^{\prime\prime}(x) equal to?
Consider the following for the next two (02) items that follow : Let f(x) and g(x) be two functions such that g(x)=x-\frac{1}{x} and f \circ g(x)=x^{3}-\frac{1}{x^{3}}.
- A. -\frac{2}{x^{3}}
- B. 2x+\frac{2}{x^{3}}
- C. 6x+3
- D. 6x ✓
Correct Answer: D. 6x
Explanation
From the previous question, we established that f(x) = x^3 + 3x. Differentiating once gives f'(x) = 3x^2 + 3. Differentiating a second time yields f''(x) = 6x.
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