5.3 The Fundamental Theorem of Calculus/15

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y=\int _{0}^{tan(x)}{\sqrt {t+{\sqrt {t}}}}\,dt}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}{\frac {d}{dx}}(y)={\frac {d}{dx}}\left[\int _{0}^{tan(x)}{\sqrt {t+{\sqrt {t}}}}\,dt\right]=\sec ^{2}(x)\cdot {\sqrt {tan(x)+{\sqrt {tan(x)}}}})-0\cdot {\sqrt {0+{\sqrt {0}}}}\,=\sec ^{2}(x)\cdot {\sqrt {tan(x)+{\sqrt {tan(x)}}}})\end{aligned}}}

${\text{Therefore, }}y'=\sec ^{2}(x)\cdot {\sqrt {tan(x)+{\sqrt {tan(x)}}}})$