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B Substitution error?

  1. Jan 22, 2017 #1
    I'm learning about derivatives and on the website they put the value

    x^2 into f(x + dx) and it became
    (x + dx)^2

    Shouldn't it be (x^2 + dx^2) ?

    It's the last example

    https://www.mathsisfun.com/calculus/derivatives-dy-dx.html

    Thanks in advance!
     
  2. jcsd
  3. Jan 22, 2017 #2

    phyzguy

    User Avatar
    Science Advisor

    You're thinking of it wrong. The function f(x) = x^2 says, "take the input value and square it". So f(x+dx) means "take (x+dx) and square it", which is (x+dx)^2.
     
  4. Jan 22, 2017 #3
    That makes sense thank you
     
  5. Jan 22, 2017 #4

    Mark44

    Staff: Mentor

    They aren't "putting the value x^2 into f(x + dx)" -- they are saying that ##f(x) = x^2## and are then calculating ##f(x + dx)## (or more likely, ##f(x + \Delta x)## ). As phyzguy noted, the given function squares its input value, so ##f(x + \Delta x) = (x + \Delta x)^2 \ne x^2 + (\Delta x)^2##.
     
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