Chapter 5 - The Integral - 5.5 The Fundamental Theorem of Calculus, Part II - Exercises - Page 263: 33

${2x}{tan(x^{2})}-\frac{tan\sqrt x}{2\sqrt x}$

$G(x)$ = $\int_{\sqrt x}^{x^{2}}tan(t)dt$ = $\int_{0}^{x^{2}}tan(t)dt$ - $\int_{0}^{\sqrt x}tan(t)dt$ apply chain rule with FTC we get $G'(x)$ = $tan(x^{2})(2x)-tan(\sqrt x)(\frac{1}{2}x^{-\frac{1}{2}})$ = ${2x}{tan(x^{2})}-\frac{tan\sqrt x}{2\sqrt x}$