Calculate ddxarctan(ex2)\frac{d}{dx} \arctan(e^{x^2})dxdarctan(ex2).
2xex21+e2x2\frac{2xe^{x^2}}{1 + e^{2x^2}}1+e2x22xex2
ex21+ex4\frac{e^{x^2}}{1 + e^{x^4}}1+ex4ex2
2x1+e2x2\frac{2x}{1 + e^{2x^2}}1+e2x22x
xex21+e2x2\frac{xe^{x^2}}{1 + e^{2x^2}}1+e2x2xex2