Find the second order derivatives of the function f(x) exsin⁡xcos⁡2x

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Find the second order derivatives of the function f(x)  exsin⁡xcos⁡2x

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Step 1 Givenexsin⁡xcos⁡2xStep 2 Finding the second order derivativesLet f(x)=exsin⁡xcos⁡2x=12ex(2cos⁡2xsin⁡x)=12ex(sin⁡3x−sin⁡x)Differentiating w.r.t xf′(x)=ex2[3cos⁡3x−cos⁡x]+12(sin⁡3x−sin⁡x)ex=ex2(3cos⁡3x−cos⁡x+sin⁡3x−sin⁡x)Again Differentiating w.r.t xf″(x)=ex2(−9sin⁡3x+sin⁡x+3cos⁡3x−cos⁡x)+12(3cos⁡3x−cos⁡x+sin⁡3x−sin⁡x)ex=ex2[6cos⁡3x−8sin⁡3x−2cos⁡x]=ex(3cos⁡3x−4sin⁡3x−cos⁡x)

Find the second order derivatives of the function f(x) exsin⁡xcos⁡2x

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