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Question Number 170255 by mathlove last updated on 19/May/22

$$\frac{d}{dx}[{\int }_2^x{e}^{t^2}dt=?$$

Answered by floor(10²Eta[1]) last updated on 19/May/22

$${\int }_2^{\mathrm{x}}{\mathrm{e}}^{{\mathrm{t}}^2}\mathrm{dt}=\mathrm{F}\left(\mathrm{x}\right)-\mathrm{F}\left(2\right)$$$$\frac{\mathrm{d}}{\mathrm{dx}}{\int }_2^{\mathrm{x}}{\mathrm{e}}^{{\mathrm{t}}^2}\mathrm{dt}=\frac{\mathrm{d}}{\mathrm{dx}}\mathrm{F}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)={\mathrm{e}}^{{\mathrm{x}}^2}$$

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