1.f(x)=∫& lt； 0，x & gt(x-t)e^(-t^2)dt =∫& lt； 0，x & gtxe^(-t^2)dt-∫& lt； 0，x & gtte^(-t^2)dt

= x∫& lt； 0，x & gte^(-t^2)dt-∫& lt； 0, x & gtTe (-t 2) dt (for t integral, x is relative to a constant, which can be mentioned outside the integral sign).

f '(x)=∫& lt； 0，x & gte^(-t^2)dt+xe^(-x^2)-xe^(-x^2)=∫& lt； 0，x & gte^(-t^2)dt

df(x)= f '(x)dx =[∫& lt； 0，x & gte^(-t^2)dt] dx

2.dy/dx = y ' & lt； t & gt/x ' & lt； T> when = 3t 2/(2t) = (3/2) t and t = 2, the tangent slope k = (3/2)t = 3,

Tangent point (5,8), tangent equation y-8 = 3(x-5), that is, 3x-y-7 = 0.