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Lost learning derivatives

  1. Feb 22, 2006 #1
    Hello, today my teacher presented us with the concept of derivatives. I was okay in class, but when I got home, I was completly lost. Using the definition (f(x+h) - f(x))/h, we have to fine the derivative of y=2x^2 - 5. I know the answer is 4x from the back of the book, but I cant understand how to get it. Am I factoring something wrong? I get to a point of simplification that everything just cancels out. Your help is greatly appriciated!
     
  2. jcsd
  3. Feb 22, 2006 #2
    The definition you want to use is this:

    [tex]\lim_{h\rightarrow 0}\frac{f(x+h) - f(x)}{h}[/tex]

    Now, set [itex]f(x)=2x^2-5[/itex] and insert this in the expression, simplify and take the limit.
     
  4. Feb 22, 2006 #3
    Quick check: When you expand the numerator, f(x+h)-f(x), you should get an expression that cancels the h in the denominator.

    -Dan
     
  5. Feb 22, 2006 #4
    my problem is when i simplify, i get 0 over 0....i dont know why....i cant get the h to go away in the denominator
     
  6. Feb 22, 2006 #5
    [tex] f(x+h)=2(x+h)^2-5=2x^2+4xh+2h^2-5 [/tex]
    and
    [tex] f(x)=2x^2-5 [/tex]
    So when you subtract the two you get...

    -Dan
     
    Last edited: Feb 22, 2006
  7. Feb 22, 2006 #6
    Then you must be doing something wrong. Remember this: If [itex]f(x)=2x^2-5[/itex], what is then [itex]f(x+h)[/itex]? Check your calculations again.
     
  8. Feb 22, 2006 #7
    Thank you so much guys!!! Wow i feel dumb....turns out i was just plugging the functions in wrong. Thank you so much!!!!
     
  9. Feb 22, 2006 #8
    Hey, as I always tell my students: it's only a dumb question when you DON'T ask it! :biggrin:

    -Dan
     
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