d/dx∫[x^2→0]xsin(t^2)dt

d/dx∫[x^2→0]xsin(t^2)dt=∫[x^2→0]sin(t^2)dt-2(x^2)sin(x^4),(x^2是下限,是上限取+号）求详细过程1).∫[x^2→0]xsin(t^2)dt=x*∫[x^2→0]sin(t^2)dt,用乘积求导法则。2）（∫[x^2→0]sin(t^2)dt)'用积分限函数求导公式，但积分限是x^2，用复合函数求导法则。是（∫[x^2→0]sin(t^2)dt)'=-2(x^2)sin(x^4), 。