Question:medium
If $f(x) = \dfrac{x + \cos x}{x - \cos x}$, then $f'\!\left(\dfrac{\pi}{2}\right)$ equals
If $f(x) = \dfrac{x + \cos x}{x - \cos x}$, then $f'\!\left(\dfrac{\pi}{2}\right)$ equals
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Quotient rule: $\left(\dfrac{u}{v}\right)' = \dfrac{u'v - uv'}{v^2}$. Evaluate trigonometric values carefully at the given point.
Updated On: Apr 8, 2026
- $\dfrac{2}{\pi}$
- $\dfrac{-2}{\pi}$
- $\dfrac{4}{\pi^2}$
- $\dfrac{-4}{\pi^2}$
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The Correct Option is D
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