SOLUTION: DIFFERENCIATION: IF Y=1/1+X,SHOW THAT (1+X)d2y/dx2+2dy/dx=0

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Question 10625: DIFFERENCIATION:
IF Y=1/1+X,SHOW THAT
(1+X)d2y/dx2+2dy/dx=0
Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
Y = (1+x)^(-1)
dy/dx = (-1)(1+x)^(-2)
d2y/dx2 = (-1)(-2)(1+x)^(-3) = (-2)[((-1)(1+x)^(-2)](1+x)^(-1)

d2y/dx2 = (-2)dy/dx [(1+x)^(-1)]
(1+x)d2y/dx2 = -2dy/dx
(1+x)d2y/dx2 + 2dy/dx = 0