Approximate value of delta-y

Dear experts,

In the attached screen I have shown the text from ‘application of derivatives’ discussing the calculation of approximate values of delta-n.

Can someone please explain the steps n text between 2 and 3.

I am having a challenge to understand how delta-x=delta-y has been arrived by the substitution.

Thank you
ExcellearnerAsked:
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ExcellearnerAuthor Commented:
Dear experts,

Please find attached the pic i was referring to.

kindly help.

Thank you
WhatsApp-Image-2018-02-24-at-14.28.2.pdf
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d-glitchCommented:
This line is clearly in error:
    If we take y = f(x) = x in (1)    

y = f(x)  is true by definition      But neither y nor f(x) is equal to x.  And none of these terms is relevant to Eq (1).

I think the point of all this is to understand that derivative of the function f(x) at x is (approximately equal) or (equal in the limit) to the slope as defined by delta_x/delta_ y (where delta is the little differential triangle).
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