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Given a derivative, find other ones

  1. Oct 17, 2006 #1
    If the derivative of y = k(x) equals 2 when x = 1, what is the derivative of

    (a) k(2x) when x = 1/2?
    (b) k(x+1) when x = 0?
    (c) k ((1/4)x) when x = 4?


    Here is my work:
    k'(1) = 2

    (a) k'(2x) = ?
    k'(2(1/2)) = ?
    k'(1) = 2

    (b) k'(x+1) = ?
    k'(0+1) = ?
    k'(1) = 2

    (c) k'((1/4)x) = ?
    k'((1/4)(4)) = ?
    k'(1) = 2

    Is the answer for every question 2?

    I just find it strange that this question would be that easy, so naturally I think I approached it incorrectly.

    Please tell me if it is correct.

    Thanks.
     
  2. jcsd
  3. Oct 17, 2006 #2
    no you have to use the chain rule.

    the derivative of [tex]k(2x)[/tex] is [tex] k'(2x)(2) [/tex] So its [tex] k'(1)(2) = 4 [/tex]
     
    Last edited: Oct 17, 2006
  4. Oct 17, 2006 #3
    All right, let's try this again:

    (a) [tex] k'(2x) = k'(2x)(2) = k'(1)(2) = 4 [/tex]

    (b) [tex] k'(x+1) = k'(x+1)(1) = k'(1)(1) = 2 [/tex]

    (c) [tex] k'(\frac{1}{4}x) = k'(\frac{1}{4}x)(\frac{1}{4}) = k'(1)(\frac{1}{4}) = \frac{1}{2} [/tex]
     
  5. Oct 17, 2006 #4
    yes that is correct
     
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