Differentiation: A sign question.
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Differentiation: A sign question.

[From: ] [author: ] [Date: 11-06-19] [Hit: ]
without seeing the whole question I cant know for sure ..thirdlyI have many mistakes in textbooks I just found one recently in a question and asked on yahoo for comfirmation ifIwas correct and the book incorrect sothe book may be incorrect sodont get upset ifit is justargue your pointsee what the teacher says........
It was a longer question but one part involved me differentiating: "-2xy."
I took this to be -2x(dy/dx) -2y, but the mark-scheme says it's "-2x(dy/dx) + 2y". Why is it +2y??

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x^3 − 2xy − 4x + y^3 − 51 = 0<==== start differentiation

3x^2 − 2(x * y' + y * 1 ) − 4 + 3y^2 * y' = 0

3x^2 − 2xy' - 2y − 4 + 3y^2 * y' = 0

3x^2 - 2y − 4 = 2xy' - 3y^2 * y'

3x^2 - 2y − 4 = y' * (2x - 3y^2)

(3x^2 - 2y − 4) / (2x - 3y^2) = y' = m ====> at the point (4 , 3)

(3 * 4^2 - 2 * 3 − 4) / (2 * 4 - 3 * 3^2) = m

-2 = m <=== perpendicular as 1/2

y = mx + b <===== at (4 , 3)
3 = (1/2) * 4 + b
3 = 2 + b
3 - 2 = b
1 = b

y = (1/2)x + 1

-(1/2)x + y - 1 = 0


-x + 2y - 2 = 0

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you should put the whole question down i think there may have been a negative sign the other person is incorrect .

if you differentiate -2xy

-2x*dy/dx -2y*dx/dx
= -2x(dy/dx) - 2y

now that is the answer but you may have forgotten a exponent
or there may have been a 4y from another section that adds to -2y to give 2y


without seeing the whole question I cant know for sure ..

thirdly I have many mistakes in textbooks I just found one recently in a question and asked on yahoo for comfirmation if I was correct and the book incorrect so the book may be incorrect so dont get upset if it is just argue your point see what the teacher says..

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i think it must be
- [2x ( dy / dx) + 2y]
1
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