5.3 The Fundamental Theorem of Calculus/13

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 h(x)=\int_{2}^{1/x}\arctan(t)dt}

${\frac {d}{dx}}\left[h(x)\right]={\frac {d}{dx}}\left[\int _{2}^{1/x}\arctan(t)dt\right]={\frac {-1}{x^{2}}}\cdot \left(\arctan \left({\frac {1}{x}}\right)\right)-0\cdot (\arctan \left(2)\right)={\frac {-\arctan {\frac {1}{x}}}{x^{2}}}$

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 \text{Therefore, } h'(x)=\frac{-\arctan\frac{1}{x}}{x^2}}