5.3 The Fundamental Theorem of Calculus/13

$h(x)=\int _{2}^{1/x}\arctan(t)dt$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}\left[h(x)\right]=\frac{d}{dx}\left[\int_{2}^{1/x}\arctan(t)dt\right]=\frac{-1}{x^2}\cdot(\arctan\left(\frac{1}{x}\right))-0\cdot(\arctan\left(2)\right)=\frac{-arctan\frac{1}{x}}}

${\text{Therefore, }}g'(x)=$