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- Homework Statement
- Expand the function ##f(x)=\sin x / (\cosh x + 2)## in a Taylor series around the origin going up to ##x^3##

- Relevant Equations
- ##f(x)=f(a)+f^{(1)}(a)(x-a)+\frac{1}{2!}f(2)(a)(x-a)^2+...##

First I got ##f(0)=0##,

Then I got ##f'(x)(0)=\frac{\cos x(2+\cosh x)-\sin x\sinh x}{(2+\cosh x)^2}=1/3##

But when I tried to got ##f''(x)## and ##f'''(x)##, I felt that's terrible, If there's some easy way to get the anwser?

Then I got ##f'(x)(0)=\frac{\cos x(2+\cosh x)-\sin x\sinh x}{(2+\cosh x)^2}=1/3##

But when I tried to got ##f''(x)## and ##f'''(x)##, I felt that's terrible, If there's some easy way to get the anwser?

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