Hmmm. Your question is ill worded. I suspect you mean g(x) is the integral of e^(3t^2)-3t dt from 4 to x.
Otherwise, we'd need the integral of e^(3t^2) which is not elementary.
So, with that in mind,
dg/dx = e^(3x^2)-3x
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
g(x) = e^(3t^2) − 3t dt from 4 to x
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