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TS EAMCET · Maths · Differentiation

If \(f(x)=(\cos x)(\cos 2 x) \ldots(\cos n x)\) then \(f^{\prime}(x)+\sum_{r=1}^n(r \tan r x) f(x)\) is equal to

  1. A \(f(x)\)
  2. B 0
  3. C \(-f(x)\)
  4. D \(2 f(x)\)
Verified Solution

Answer & Solution

Correct Answer

(B) 0

Step-by-step Solution

Detailed explanation

\(f(x)=(\cos x)(\cos 2 x) \ldots(\cos n x)\) \(f^{\prime}(x)=-\sin x \cdot \cos 2 x \ldots \cos n x\) \(+\cos x \frac{d}{d x}\{\cos 2 x \cdot \cos 3 x \ldots \cos n x\}\) \(f^{\prime}(x)=-\sin x \cdot \cos 2 x \ldots \cos n x\)…