If f(x)=sin(x³), find the value of its 2001st derivative, at x=0.
Why is this problem a D4? Is the difficulty rated for knowing and knowing how to derive the Taylor expansion of the sine function? Or proving its convergence at x=0 and the validity of term by term differentiation? As well as going back to the roots of proving that the 2001st derivative exist?
I do not really see any real problem by simple and direct application of the Taylor expansion of the sine function.
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