5.3 The Fundamental Theorem of Calculus/15

Use part 1 of the FTC to find the derivative of the function: $y=\int _{0}^{tan(x)}{\sqrt {t+{\sqrt {t}}}}\,dt$

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 \begin{align} y=\int_{0}^{tan(x)}\sqrt{t+\sqrt t}\,dt =\sqrt{tan(x)+\sqrt tan(x)}\cdot\sec^{2}(x) \end{align} }

FTC 1: Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {d}{dx}}\int _{a(x)}^{b(x)}f(t)\,dt=b^{\prime }(x)\cdot \,f(b(x))-\,a^{\prime }(x)\cdot \,f(a(x))}