Question

求三道题的解题过程





Answer 1

(1)
xy=e^(x+y)
y+ xy' = (1+y')e^(x+y)
[x-e^(x+y) ]y' = e^(x+y) -y
y' = [e^(x+y) -y]/[x-e^(x+y) ]
(2)
x+2y-cosy =0
1+2y' +siny .y' =0
(2+siny) y' = -1
y' = -1/(2+siny)
y'' = cosy . y'/(2+siny)^2
= cosy . [-1/(2+siny)]/(2+siny)^2
= -cosy/(2+siny)^3
(3)
y= √(x+2) .(3-x)^4 /(x+1)^5
lny = (1/2)ln(x+2) + 4ln(3-x) - 5ln(x+1)
(1/y)y' = 1/[2(x+2)] - 4/(3-x) - 5/(x+1)

y' = {1/[2(x+2)] - 4/(3-x) - 5/(x+1)} . {√(x+2) .(3-x)^4 /(x+1)^5 }