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 x- 3x. This function must be differentiated first:

d/dx (x2 - 3x) = 2x - 3

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

d/dz (ez) = e 

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

dy/dx = (2x - 3)e= (2x - 3)ex^2 - 3x

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