Question

∫(0到y)e^t^2dt+∫(0到x^2)sint/根号tdt=1确定关于x的函数求dy/dx？

∫(0到y)e^t^2dt+∫(0到x^2)sint/根号tdt=1确定关于x的函数求dy/dx

Answer 1

∫(0,y)e^t²dt+∫(0,x²)sint/√tdt=1
d/dx∫(0,y)e^t²dt+d/dx∫(0,x²)sint/√tdt=0
e^y²·y'+sinx²/√x²·(x²)'=0
e^y²·y'+sinx²/√x²·2x=0
dy/dx=y'=2sinx²/e^y²