h ( x ) = ∫ 2 1 / x arctan ( t ) d t {\displaystyle h(x)=\int _{2}^{1/x}\arctan(t)dt}
d d x [ h ( x ) ] = d d x [ ∫ 2 1 / x arctan ( t ) d t ] = − 1 x 2 ⋅ ( arctan ( 1 x ) ) {\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)}
![{\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)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/2e1b1922b9c91748a19e10fc8c3b4c022df3d78c)