Different result by hand-differentiaion vs MATLAB diff() function.
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I differentiated the equation, ( K=(y^2 + 2*y + 2)/(y + 1)^2 ), by hand-differentiation and got result, ( -2/(y+1) ) while the result with MATLAB function, ( diff(K, y) ) was, (2*y + 2)/(y + 1)^2 - (2*(y^2 + 2*y + 2))/(y + 1)^3
I don't know why was it and what was the wrong I did.
Please help. Thank you.
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Roger Stafford
2018-3-5
编辑：Roger Stafford
2018-3-5
0 个投票
Your "hand-differentiation" is not correct! The 'diff' answer is correct but can be simplified to an equivalent -2/(y+1)^3. (Perhaps the latter is what you meant to write?)
5 个评论
yf
2018-3-5
Roger Stafford
2018-3-5
编辑：Roger Stafford
2018-3-5
Here is the differentiation computation:
K = (y^2 + 2*y + 2)/(y + 1)^2
dK/dy = (d(y^2 + 2*y + 2)/dy)/(y+1)^2 + (d((y+1)^-2)/dy)*(y^2 + 2*y + 2)
= (2*y+2)/(y+1)^2 - 2*((y+1)^-3)*(y^2 + 2*y + 2)
= ((2*y+2)*(y+1)-2*(y^2 + 2*y + 2))/(y+1)^3
= ((2*y^2+4*y+2)-(2*y^2+4*y+4)) / (y+1)^3
= -2/(y+1)^3
Somehow you lost the cube power in that y+1 denominator.
Stephen23
2018-3-5
@yf: considering that Roger Stafford helped you to resolve this issue then you should accept this answer: this is the easiest way for you to show your appreciation to the volunteers who help you on this forum.
Stephen23
2018-3-5
Hi Mr. Roger Stafford,
I found the problem now. the denominator in the solution manual is actually,
(y^2 + 2*y + 1)^2 = ( (y + 1)^2 )^2
hence is,
(2*y + 2)/(y + 1)^2 - (2*(y^2 + 2*y + 2))/(y + 1)^3 = -2*(y + 1)/(y+1)^4 = -2/(y+1)^3
I made mistake on this point.
Thank you so much for you answer and help.
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