ExamBro
ExamBro
AP 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

Given that On differentiating w.r.t. \(x\), we get \(f^{\prime}(x)=-10 \sin x+(13+2 x) \cos x+2 \sin x\) Again differentiating, we get \(\begin{aligned} f^{\prime \prime}(x)=-10 \cos x-(13+2 x) \sin x+ & 2 \cos x \\ & +2 \cos x ...(ii) \end{aligned}\) On adding Eqs. (i) and…