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Thread: First-Order Derivative

  1. September 27th 2010, 04:45 PM #1
    jcrane
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    First-Order Derivative

    I'm not sure if i'm doing this right, it's been awhile since i've had to deal with calculus!
    So it says calculate the first-order derivative with respect to x:

    a. y = 3x^2
    Ans: F(x) = 9X^2

    b. y = x^3
    Ans: F(x) 3x^2

    c. y=mx + b
    Ans: Not sure on this one ..

    d. y = 1/x
    Ans: Also not sure

    e. y = 37x^4
    Ans: F(x) = 148x^3

    f. y = x^a/b
    ANS: F(x) = a/b x^a/b - 1

    Okay. maybe i'm completely wrong with some of these!
    any help is greatly appreciated!
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  2. September 27th 2010, 05:21 PM #2
    TheCoffeeMachine
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    a. y = 3x^2
    Ans: F(x) = 9X^2
    Recheck.

    Quote Originally Posted by jcrane View Post
    c. y=mx + b
    Ans: Not sure on this one ..
    m and b are constant, just like any other.

    d. y = 1/x
    Ans: Also not sure
    \frac{1}{x} = x^{-1}.
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  3. September 27th 2010, 05:22 PM #3
    pickslides
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    Recall y= x^n \implies \frac{dy}{dx}= nx^{n-1}

    Quote Originally Posted by jcrane View Post
    a. y = 3x^2
    Ans: F(x) = 9X^2


    Therefore

    \frac{dy}{dx}=9x

    Quote Originally Posted by jcrane View Post


    b. y = x^3
    Ans: F(x) 3x^2

    Yep


    Quote Originally Posted by jcrane View Post




    c. y=mx + b
    Ans: Not sure on this one ..

    treat m and b as a constant,




    Quote Originally Posted by jcrane View Post

    d. y = 1/x
    Ans: Also not sure
    \frac{1}{x}= x^{-1}
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  4. September 28th 2010, 07:23 PM #4
    pirateboy
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    Err...pickslides, I think you made a "silly mistake" on the first one.

    \frac{d}{dx}\left(3x^2\right) = 2\cdot 3x^{2-1}\neq 9x
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