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Thread: Applying chain rule

  1. #1
    Member VitaX's Avatar
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    Applying chain rule

    Find the derivative of the following:

    $\displaystyle y = (2x - 5)(4 - x)^{-1}$

    I got $\displaystyle y' = 2x(4 - x)^{-1} + (2x - 5)(4 - x)^{-2}$ or $\displaystyle y' = \frac{2x}{4 - x} + \frac{2x - 5}{(4 - x)^2}$

    Correct?
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  2. #2
    MHF Contributor Matt Westwood's Avatar
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    Quote Originally Posted by VitaX View Post
    Find the derivative of the following:

    $\displaystyle y = (2x - 5)(4 - x)^{-1}$

    I got $\displaystyle y' = 2x(4 - x)^{-1} + (2x - 5)(4 - x)^{-2}$ or $\displaystyle y' = \frac{2x}{4 - x} + \frac{2x - 5}{(4 - x)^2}$

    Correct?
    $\displaystyle y' = 2x(4 - x)^{-1} + (2x - 5)(4 - x)^{-2}$ or $\displaystyle y' = \frac{2x}{4 - x} + \frac{2x - 5}{(4 - x)^2}$ looks wrong to me.

    You've got your product rule okay, but when you differentiated $\displaystyle 2x-5$ you got $\displaystyle 2x$ rather than $\displaystyle 2$.

    A simple slip-up, it's so easy to do - other than that the technique is fine.
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  3. #3
    Member VitaX's Avatar
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    Quote Originally Posted by Matt Westwood View Post
    $\displaystyle y' = 2x(4 - x)^{-1} + (2x - 5)(4 - x)^{-2}$ or $\displaystyle y' = \frac{2x}{4 - x} + \frac{2x - 5}{(4 - x)^2}$ looks wrong to me.

    You've got your product rule okay, but when you differentiated $\displaystyle 2x-5$ you got $\displaystyle 2x$ rather than $\displaystyle 2$.

    A simple slip-up, it's so easy to do - other than that the technique is fine.
    ah so I did. Thanks for the help.
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  4. #4
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    Quote Originally Posted by VitaX View Post
    Find the derivative of the following:

    $\displaystyle y = (2x - 5)(4 - x)^{-1}$

    I got $\displaystyle y' = 2x(4 - x)^{-1} + (2x - 5)(4 - x)^{-2}$ or $\displaystyle y' = \frac{2x}{4 - x} + \frac{2x - 5}{(4 - x)^2}$

    Correct?
    Personally, I'd use the quotient rule since $\displaystyle y = \frac{2x - 5}{4 - x}$.
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  5. #5
    Member VitaX's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Personally, I'd use the quotient rule since $\displaystyle y = \frac{2x - 5}{4 - x}$.
    Yah works a lot better and easier here. Final answer is $\displaystyle y' = \frac{3}{(4 - x)^2}$
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