What is \frac{dy}{dx} equal to?
Consider the following for the two (02) items that follow : Let y=\sin^{-1}(x-\frac{4x^{3}}{27}).
- A. \frac{1}{\sqrt{9-x^{2}}}
- B. \frac{1}{\sqrt{3-x^{2}}}
- C. \frac{3}{\sqrt{9-x^{2}}} ✓
- D. \frac{9}{\sqrt{9-x^{2}}}
Correct Answer: C. \frac{3}{\sqrt{9-x^{2}}}
Explanation
From the previous evaluation, y = 3\sin^{-1}(x/3). Differentiating with respect to x gives \frac{dy}{dx} = 3 \cdot \frac{1}{\sqrt{1 - (x/3)^2}} \cdot \frac{1}{3} = \frac{1}{\sqrt{1 - x^2/9}} = \frac{1}{\frac{\sqrt{9-x^2}}{3}} = \frac{3}{\sqrt{9-x^2}}.
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