Question:
\( \frac{d}{dx} \left( \cos^{-1}x \right) \) is:
\( \frac{d}{dx} \left( \cos^{-1}x \right) \) is:
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The derivative of \( \cos^{-1}x \) is \( -\frac{1}{\sqrt{1 - x^2}} \), which is important for solving problems involving inverse trigonometric functions.
Updated On: Feb 2, 2026
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Solution and Explanation
Step 1: Using the derivative of the inverse cosine function.
The derivative of \( \cos^{-1}x \) is a standard result: \[ \frac{d}{dx} \left( \cos^{-1}x \right) = -\frac{1}{\sqrt{1 - x^2}} \] Step 2: Conclusion.
Thus, the derivative of \( \cos^{-1}x \) is \( -\frac{1}{\sqrt{1 - x^2}} \).
The derivative of \( \cos^{-1}x \) is a standard result: \[ \frac{d}{dx} \left( \cos^{-1}x \right) = -\frac{1}{\sqrt{1 - x^2}} \] Step 2: Conclusion.
Thus, the derivative of \( \cos^{-1}x \) is \( -\frac{1}{\sqrt{1 - x^2}} \).
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