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
- A \(f(x)\)
- B 0
- C \(-f(x)\)
- D \(2 f(x)\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
\(f(x)=(\cos x)(\cos 2 x) \ldots(\cos n x)\) \(f^{\prime}(x)=-\sin x \cdot \cos 2 x \ldots \cos n x\) \(+\cos x \frac{d}{d x}\{\cos 2 x \cdot \cos 3 x \ldots \cos n x\}\) \(f^{\prime}(x)=-\sin x \cdot \cos 2 x \ldots \cos n x\)…
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