If $p(x)={\int }_2^{x^3}\sin tdt$, find $p^{\prime }\left(x\right)$.

If $F(x)={\int }_{3x}^{\cos x}{e}^{t^2}dt$, find $F^{\prime }\left(x\right)$.

If $p(x)={\int }_3^{e^x}{e}^{t^2}dt$, find $p^{\prime }\left(x\right)$.

If $p(x)={\int }_0^x\left(t^3-7t\right)dt$, find $p^{\prime \prime }\left(x\right)$.

If $G(x)={\int }_3^{x^2}\sin tdt$, find $G^{\prime }\left(x\right)$.

If $g(x)={\int }_1^x{e}^{t^2}dt$, find $g^{\prime }\left(x\right)$.

If $p(x)={\int }_1^{\cos x}\cos \left(t^2\right)dt$, find $p^{\prime }\left(x\right)$.

If $q(x)={\int }_5^x\ln \left(t^2+1\right)dt$, find $q^{\prime }\left(x\right)$.

If $H(x)={\int }_4^x\ln \left(t^2+1\right)dt$, find $H^{\prime \prime }\left(x\right)$.

If $p(x)={\int }_0^x\left(t^5-t\right)dt$, find $p^{\prime \prime }\left(x\right)$.

If $g(x)={\int }_x^3\cos \left(t^2\right)dt$, find $g^{\prime }\left(x\right)$.

If $G(x)={\int }_x^5\sin tdt$, find $G^{\prime }\left(x\right)$.

If $G(x)={\int }_{4x}^{\sqrt{x}}{e}^{t^2}dt$, find $G^{\prime }\left(x\right)$.

If $q(x)={\int }_2^{x^2}\ln \left(t^2+1\right)dt$, find $q^{\prime }\left(x\right)$.

If $g(x)={\int }_3^x{e}^{t^2}dt$, find $g^{\prime \prime }\left(x\right)$.

If $H(x)={\int }_2^{x^3}\sqrt{t^3+1}dt$, find $H^{\prime }\left(x\right)$.

If $g(x)={\int }_x^2\ln \left(t^2+1\right)dt$, find $g^{\prime }\left(x\right)$.

If $p(x)={\int }_2^{4x}\left(t^2-9\right)dt$, find $p^{\prime }\left(4\right)$.

If $G(x)={\int }_3^{4x}{e}^{t^2}dt$, find $G^{\prime }\left(x\right)$.

If $H(x)={\int }_3^x\sqrt{t^3+1}dt$, find $H^{\prime }\left(x\right)$.

If $g(x)={\int }_x^2\frac{1}{t^2+1}dt$, find $g^{\prime }\left(x\right)$.

If $G(x)={\int }_{5x}^{x^3}{e}^{t^2}dt$, find $G^{\prime }\left(x\right)$.

If $q(x)={\int }_0^{e^x}\ln \left(t^2+1\right)dt$, find $q^{\prime }\left(x\right)$.

If $H(x)={\int }_2^x\frac{1}{t^2+1}dt$, find $H^{\prime }\left(x\right)$.

If $g(x)={\int }_4^x\sin tdt$, find $g^{\prime }\left(x\right)$.

If $F(x)={\int }_3^{5x}\left(t^2-5\right)dt$, find $F^{\prime }\left(2\right)$.

If $p(x)={\int }_0^{2x}\left(t^2-8\right)dt$, find $p^{\prime }\left(3\right)$.

If $G(x)={\int }_x^1\sin tdt$, find $G^{\prime }\left(\frac{\pi }{2}\right)$, with $x$ in radians.

If $q(x)={\int }_3^x\frac{1}{t^2+1}dt$, find $q^{\prime }\left(1\right)$.

If $p(x)={\int }_3^{4x}\left(t^2-3\right)dt$, find $p^{\prime }\left(1\right)$.