求dy/dx,y=∫sin(t^2)dt由1/x积到根号x

题目

求dy/dx,y=∫sin(t^2)dt由1/x积到根号x

答案

d/dx ∫(1/x→√x) sin(t²) dt
= d(√x)/dx · sin(√x²) - d(1/x)/dx · sin(1/x²)
= 1/(2√x) · sin|x| - (- 1/x²) · sin(1/x²)
= (sinx)/(2√x) + [sin(1/x²)]/x²