Question

高等数学求导，求过程

求一个过程，谢谢啦

Answer 1

7.dx=（et*sint+et*cost）*dt，dy=（et*cost-et*sint）*dt；dy/ds=（cost-sint）/（cost+sint）;当t=π/3时，dy/ds=（cosπ/3-sinπ/3）/（cosπ/3+sinπ/3）=√3-2

Answer 2

7. dy/dx = (dy/dt)/(dx/dt) = e^t(cost-sint)/[e^t(cost+sint)] = (1-tant)/(1+tant)

t = π/3 时，dy/dx = (1-√3)/(1+√3) = -(1/2)(√3-1)^2 = √3-2
8. dy/dx = sinx + xcosx - sinx = xcosx, x = π/3 时，dy/dx = π/6
9. y' = 2x, 在 点(1, 1), k = y'(1) = 2, 切线方程 y = 2(x-1)+1 = 2x-1
10 y' = -(1/2)x^(-3/2), 在 点(1, 1), k = y'(1) = -1/2,
切线方程 y = -(1/2)(x-1)+1 , 即 x+2y-3 = 0

追问

非常感谢！