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Thread: Power of a function rule v.s. chain rule

  1. #1
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    Question Power of a function rule v.s. chain rule

    Hi,

    I'm hoping that someone can provide some insight on the following definition:
    Power of a function rule v.s. chain rule-screen-shot-2017-08-01-8.35.17-pm.png
    I'm wanting to understand how this rule is really any different from the chain rule. According to my textbook, the power of a function rule is a special case of the chain rule, but I don't particularly understand what is so different from other cases in which you use the chain rule. Can someone help?

    Sincerely,
    Olivia
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  2. #2
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    Re: Power of a function rule v.s. chain rule



    Same ... same

    Both are the chain rule for composite functions.

    $u = g(x)$, just different notation.
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    Re: Power of a function rule v.s. chain rule

    alright thanks
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    Re: Power of a function rule v.s. chain rule

    Quote Originally Posted by otownsend View Post
    Hi,

    I'm hoping that someone can provide some insight on the following definition:
    Click image for larger version. 

Name:	Screen Shot 2017-08-01 at 8.35.17 PM.png 
Views:	12 
Size:	40.0 KB 
ID:	37925
    I'm wanting to understand how this rule is really any different from the chain rule. According to my textbook, the power of a function rule is a special case of the chain rule, but I don't particularly understand what is so different from other cases in which you use the chain rule. Can someone help?
    What you ask is just impossible to answer.
    If $f(x)=\sin^2(x^3+1) ~\&~g(x)=\sin[(x^3+1)^2]$ then are those two functions different?
    If they are the same the we do not have two functions.
    Let's evaluate $f\left(\dfrac{3\pi}{5}\right)~\&~g\left(\dfrac{3\ pi}{5}\right)$.
    So for simplicity lets say that $\theta= \dfrac{3\pi}{5}$.
    Now if you think that $f(\theta)=g(\theta)$ please just stop at once. You most go back and learn basics.
    I am sure that you see that they are indeed difference. So how do you a calculator to aid in solving?

    In one of those, we cube $\theta$ then add one. Next square that result; finally finding the sine value of that result.
    In the other one we cube $\theta$ then add one; square that result & finally find the sine value of that number.is
    Now which one is which?

    If one does not understand function composition then the chain rule will forever remain a mystery.

    Say $u(x)=3\cos^5(x^2+6x)$ then $u'(x)=15\cos^4(x^2+6x)(-\sin(x^2+6x)(2x+6))$
    Think how we might evaluate this & reverse the order.
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