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Homework Help: Easy derivative question

  1. Nov 5, 2015 #1
    • Poster has been reminded to show more work when posting schoolwork questions
    1. The problem statement, all variables and given/known data
    derive this function

    f(x) = (2x + x^3) / sqrt(x)

    2. Relevant equations

    3. The attempt at a solution
    how can i derive this without using quotient rule? my prof is asking to do so without using it.

  2. jcsd
  3. Nov 5, 2015 #2


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    Can you rewrite it in a way that would allow you to use the product rule?
  4. Nov 5, 2015 #3


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    Staff Emeritus
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    Write ##\ \sqrt{x} \ ## as ##\displaystyle \ x^{1/2} \ ## .

    By the way, the word in English is differentiate, not derive.
  5. Nov 5, 2015 #4
    Can this be done without product / quotient rule?

    Just to remind myself of how quotient rule works...

    I got to this point after using quotient rule:
    ((2x + 7x^3) / (2(x^1/2))) / x

    How do i simplify this? Sorry I don't know how to use latex code.
  6. Nov 5, 2015 #5


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    OK, here's a hint for how to do it without the product rule either: ##x^m / x^n = x^{(m-n)} ##.
  7. Nov 5, 2015 #6
    Okay using that I got something like x^5/2 + x^1/2. It doesn't seem correct, how would i account for the binomial on the numerator? would I write another expression for x such as x^h?
    edit: I just misunderstood the question... I am allowed to use both the quotient and product rule.
  8. Nov 5, 2015 #7


    Staff: Mentor

    It's not correct, but you're not too far off. And you should end up with two terms, so I don't understand what you're asking about accounting for the binomial.
    What do you get if you carry out the division below?
    (2x + x^3) / sqrt(x)
  9. Nov 5, 2015 #8
    alright... I got it.

    I simply just subtract the exponents from the numerator and denominator so it became (2 + 5x^2) / 2x^1/2
  10. Nov 5, 2015 #9


    Staff: Mentor

    No, that's not even close. There's some very basic algebra that you need to review. If you don't, you absolutely won't be able to do calculus.

    ##\frac{(a + b)} c = (a + b) \cdot \frac 1 c = a \cdot \frac 1 c + b \cdot \frac 1 c## . Use the distributive property to multiply each term of a + b by 1/c. Can you apply this idea to your problem, ##\frac{2x + x^3}{\sqrt{x}}##?
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