Answer
$$y'=3e^{x^3}(9x^4-6x^3+2x^2+6x-2)$$
Work Step by Step
$$y=(9x^2-6x+2)e^{x^3}$$
The derivative of function $y$ is: $$y'=(9x^2-6x+2)'e^{x^3}+(9x^2-6x+2)(e^{x^3})'$$
$$y'=(18x-6)e^{x^3}+(9x^2-6x+2)e^{x^3}(x^3)'$$
$$y'=(18x-6)e^{x^3}+3x^2(9x^2-6x+2)e^{x^3}$$
$$y'=(18x-6)e^{x^3}+(27x^4-18x^3+6x^2)e^{x^3}$$
$$y'=e^{x^3}(27x^4-18x^3+6x^2+18x-6)$$
$$y'=3e^{x^3}(9x^4-6x^3+2x^2+6x-2)$$
