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Math Help - Power and Product Rule

  1. #1
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    Power and Product Rule

    Differentiate the given function (two methods)

    I only know how to do the chain rule which I get 8(4x-7)

    please show how to do this so I can master the rest of the questions my self..thanks
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  2. #2
    MHF Contributor Amer's Avatar
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    where is your function ??
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    Sorry I can't believe I did not post it:

    (7-4x)^2
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    MHF Contributor Amer's Avatar
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    you differentiate it correct there is a negative sign

    f(x)=(7-4x)^2

    f'(x)=2(-4)(7-4x)

    f(x)=(-3x^2)^{n}....f'(x)=n(-3x^2)'(-3x^2)^{n-1}=n(-3(2)(x)^{2-1})(-3x^2)^{n-1}
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    How do I show that the two answers are the same (product rule and power rule) Thanks
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    MHF Contributor Amer's Avatar
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    f(x)=(7-4x)(7-4x)

    I will differentiate it by product rule

    f'(x)=(7-4x)(-4)+(-4)(7-4x)=2(-4)(7-4x)

    in general

    f(x)=AB...A,B..functions..of..x

    differentiate

    f'(x)=A\frac{d}{dx}(B)+B\frac{d}{dx}(A)
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    What you did for the power rule..I don't understand it! Is that all the steps for it? I got the product rule that is pretty easy thanks!
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    Super Member craig's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    What you did for the power rule..I don't understand it! Is that all the steps for it? I got the product rule that is pretty easy thanks!
    Quote Originally Posted by Amer View Post
    you differentiate it correct there is a negative sign

    f(x)=(7-4x)^2

    f'(x)=2(-4)(7-4x)

    f(x)=(-3x^2)^{n}....f'(x)=n(-3x^2)'(-3x^2)^{n-1}=n(-3(2)(x)^{2-1})(-3x^2)^{n-1}
    That is the product rule, the second equation is the differentiated form of your equation, and in the third Amer is showing you how to do it for any equation.

    You take your original equation, reduce the power by 1, multiply the whole thing by the original power, this is the 2 in your equation, and then multiply the whole thing by the derivative of what's in the brackets, in your equation this is (-4).

    Hope this helps
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    I know the product rule its the power rule which I don't understand
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  10. #10
    Super Member craig's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    I know the product rule its the power rule which I don't understand
    If you have an equation y = (f(x))^n.

    Then \frac{dy}{dx} = nf'(x)(f(x))^{n-1}

    As I said:

    Quote Originally Posted by craig View Post
    You take your original equation, reduce the power by 1, multiply the whole thing by the original power, this is the 2 in your equation, and then multiply the whole thing by the derivative of what's in the brackets, in your equation this is (-4).
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    sorry I misunderstood...I've been working on calculus all day getting tired...thanks!
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    Quote Originally Posted by lisa1984wilson View Post
    I know the product rule its the power rule which I don't understand
    \begin{gathered}<br />
  \frac{{df^n }}<br />
{{dx}} = n \cdot f^{n - 1}  \cdot f' \hfill \\<br />
  \frac{{d\left( {x^3  + x} \right)^7 }}<br />
{{dx}} = 7\left( {x^3  + x} \right)^6 \left( {3x^2  + 1} \right) \hfill \\ <br />
\end{gathered}
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  13. #13
    Super Member craig's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    sorry I misunderstood...I've been working on calculus all day getting tired...thanks!
    No worries, hope it's all cleared up now
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