Answer
$$y'=e^{5x/2}\Big(\frac{5}{2}x^2-3x+3\Big)$$
Work Step by Step
$$y=(x^2-2x+2)e^{5x/2}$$
The derivative of function $y$ is: $$y'=(x^2-2x+2)'e^{5x/2}+(x^2-2x+2)(e^{5x/2})'$$
$$y'=(2x-2)e^{5x/2}+(x^2-2x+2)e^{5x/2}\Big(\frac{5x}{2}\Big)'$$
$$y'=(2x-2)e^{5x/2}+\frac{5}{2}(x^2-2x+2)e^{5x/2}$$
$$y'=e^{5x/2}\Big(2x-2+\frac{5}{2}x^2-5x+5\Big)$$
$$y'=e^{5x/2}\Big(\frac{5}{2}x^2-3x+3\Big)$$