Given that $\mathrm{f}(x) = \arctan x$, find $\mathrm{f}'(x)$; the first $3$ terms, in as

Question

Given that $\mathrm{f}(x) = \arctan x$, find $\mathrm{f}'(x)$; the first $3$ terms, in ascending power of $x$, of the Maclaurin series for $\mathrm{f}'(x)$. Hence, find the Maclaurin series of $\mathrm{f}(x)$.

Accepted Answer

(i) $\dfrac1{1+x^2}$; (ii) $1-x^2+x^4$; (iii) $\arctan x=x-\dfrac{x^3}{3}+\dfrac{x^5}{5}-\cdots$

Derivation of Maclaurin's series for arctangent

Derivation of Maclaurin's series for arctangent

Solution:

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