What is the derivative of  e^(x^2)?

The derivative of a function in the form of ${e}^{f \left(x\right)}$ is ${e}^{f \left(x\right)} \cdot \mathrm{df} \frac{x}{\mathrm{dx}}$
Hence $d \frac{{e}^{{x}^{2}}}{\mathrm{dx}} = 2 \cdot x \cdot {e}^{{x}^{2}}$