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Pulling fractional exponents out of an expression

  1. Oct 22, 2016 #1
    1. The problem statement, all variables and given/known data
    Find critical numbers of the function: F(x)=t^3/4 - 2t^1/4
    Derivative I got: F'(x)=3/4 t^-1/4 - 1/2 t^-3/4

    2. Relevant equations


    3. The attempt at a solution
    I have found the derivative and I understand I must pull out a t in order to find critical numbers, and run across this issue of manipulating fractional exponents too often. How do I go about this? Thankyou.
     
  2. jcsd
  3. Oct 22, 2016 #2

    Mark44

    Staff: Mentor

    Please post questions about calculus problems in the Calculus & Beyond section, not in the Precalculus section. I have moved your post.
    First off -- your two functions are functions of t, not x, so they should be written as F(t) and F'(t).

    Rewrite the derivative so that it is a product rather than a sum. In this case, factor t^(-3/4) out of both terms.
     
  4. Oct 22, 2016 #3
    So from this I get F'(t)= t^-3/4 (3/4t^1/2 - 1/2)
     
  5. Oct 22, 2016 #4

    Mark44

    Staff: Mentor

    Yes, that's correct, but even better is F'(t) = (1/4)t^(-3/4)[3t^(1/2) - 2)
    Note that when you write exponents as inline text, t^-3/4 is usually interpreted as ##\frac{t^{-3}} 4##, using the usual rules of precedence.

    This site supports the use of LaTeX (see https://www.physicsforums.com/help/latexhelp/ under the INFO menu, in Help/How-to articles).
    Using LaTeX, the derivative looks like this:
    $$F'(t) = \frac 1 4 t^{-3/4}(3t^{1/2} - 2)$$
     
  6. Oct 22, 2016 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What you wrote means ##F = \frac{1}{4} t^3 - \frac{2}{4} t^1##. If you mean ##F = t^{3/4} - 2 t^{1/4}##, then you must use parentheses (or else use LaTeX, as I just did). With parentheses you would have F = t^(3/4) - 2 t^(1/4).
     
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