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I have a function $f(x)$ expressed as $$f(x) = \sum_{k=1}^n {a_k}sin(kx)$$ and its derivative with respect to $x$ is then $$f'(x) = \sum_{k=1}^n k{a_k}cos(kx)$$

I am actually new to Mathematica and am not comprehensively familiar with its capabilities. However, I tried to write $f(x)$ asf(x_) = Sum[Table[(Subscript[a, k])*Sin[x*k], {k, 3}]which gave me $f(x)$, but I do not know how to proceed with differentiation with respect to $x$ without defining a new series again for $f'(x)$

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    $\begingroup$ f[x_]:=Sum[(Subscript[a, k])*Sin[x*k], {k, 3}], then D[f[x], x]. $\endgroup$ – Alx Oct 24 at 14:21

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