Differentiate y = e^(x^2 - 3x).

This question is an example of the chain rule for differentiating. 

Firstly, identify the inner function. In this case, it is x² - 3x. This function must be differentiated first:

d/dx (x² - 3x) = 2x - 3

Secondly, identify the outer function. In this case, it is e^z, where z = x² - 3x. This function must be differentiated second:

d/dz (e^z) = e^z  

The final differentiated result is the derivative of the inner function multiplied by the derivative of the outer function:

dy/dx = (2x - 3)e^z = (2x - 3)e^{x^2 - 3x}