设函数y=y(x)有方程∫e^t^2dt(积分从0到y)+∫cos根号下tdt(积分从x^2到1)=0(x>0),求dy/dx._数学解答

设函数y=y(x)有方程∫e^t^2dt(积分从0到y)+∫cos根号下tdt(积分从x^2到1)=0(x>0),求dy/dx.

人气：218 ℃　时间：2020-02-05 23:54:48

解答

letdF(x) = e^(x^2)dxdG(x) = cos√xdx∫(0->y)e^t^2dt+∫(x^2->1) cos√tdt =0F(y) -F(0) + G(1) - G(x^2) =0d/dx {F(y) -F(0) + G(1) - G(x^2) } =0F'(y) dy/dx - 2xG'(x^2) =0e^(y^2) dy/dx - 2xcosx =0dy/dx = 2...