TS EAMCET · Maths · Functions
\(f(x)=e^x \sin x\), then \(f^{(6)}(x)\) is equal to :
- A \(e^{6 x} \sin 6 x\)
- B \(-8 e^x \cos x\)
- C \(8 e^x \sin x\)
- D \(8 e^x \cos x\)
Answer & Solution
Correct Answer
(B) \(-8 e^x \cos x\)
Step-by-step Solution
Detailed explanation
\(f(x)=e^x \sin x\) \(\therefore f^{\prime}(x)=e^x \cos x+\sin x e^x\) \(\Rightarrow f^{\prime \prime}(x)=e^x \cos x-e^x \sin x+e^x \sin x\) \(+e^x \cos x\) \(=2 e^x \cos x\) Now, \(\quad f^{\prime \prime \prime}(x)=-2 e^x \sin x+2 e^x \cos x\) and…
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