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) $\frac{1}{1+x^2}$ ; (ii) $\sum_{k=0}^{\infty} (-1)^k x^{2k}$ , $\sum_{k=0}^{\infty} (-1)^k \frac{x^{2k+1}}{2k+1} + c$.

Derivation of Maclaurin's series for arctangent

Derivation of Maclaurin's series for arctangent