5.3 The Fundamental Theorem of Calculus/15

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

FTC 1: 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}\int_{a(x)}^{b(x)}f(t)\,dt=b^\prime{(x)}\cdot\,f(b(x))-\,a^\prime{(x)}\cdot\,f(a(x))}

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

In this problem 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 a^\prime{(x)}= 0} , so when it is multiplied by 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 f(a(x))} it will result in 0 and doesn't need to be added.