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To find the 4th derivative of f(x) at x=0, we will use the Maclaurin series expansion of f(x).

Mathematics

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To find the 4th derivative of f(x)f(x) at x=0x=0, we will use the Maclaurin series expansion of f(x)f(x).
The Maclaurin series for an even function f(x)f(x) is given by:

f(x)=f(0)+f′′(0)2!x2+f(4)(0)4!x4+…f(x) = f(0) + \frac{f''(0)}{2!}x^2 + \frac{f^{(4)}(0)}{4!}x^4 + \dots

We need to find the coefficient of x4x^4 in the Maclaurin series of f(x)f(x) and multiply it by 4!4!.

Step 1: Determine if f(x)f(x) is an even or odd function.
The function is $f(x) = \tan^{-1}\

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