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TS EAMCET · Maths · Differentiation

If \(f(x)=10 \cos x+(13+2 x) \sin x, \quad\) then \(f^{\prime \prime}(x)+f(x)\) is equal to

  1. A \(\cos x\)
  2. B \(4 \cos x\)
  3. C \(\sin x\)
  4. D \(4 \sin x\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(4 \cos x\)

Step-by-step Solution

Detailed explanation

\(f'(x) = \frac{d}{dx} [10 \cos x + (13+2 x) \sin x] = -10 \sin x + 2 \sin x + (13+2 x) \cos x = -8 \sin x + (13+2 x) \cos x\) \(f''(x) = \frac{d}{dx} [-8 \sin x + (13+2 x) \cos x] = -8 \cos x + 2 \cos x - (13+2 x) \sin x = -6 \cos x - (13+2 x) \sin x\)…