[tex]\dfrac{d}{dx} \left(e^{x^2} \cdot x^2\right)\\\\=e^{x^2} \dfrac{d}{dx} (x^2) + x^2 \dfrac{d}{dx}\left (e^{x^2}\right)\\\\=e^{x^2} \cdot 2x + x^2 \cdot e^{x^2} \cdot \dfrac{d}{dx} (x^2)\\\\=2x e^{x^2} + 2x^3 e^{x^2}\\\\=2xe^{x^2}(1+x^2)[/tex]
