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Math Help - More Chain Rule Help

  1. #1
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    More Chain Rule Help

    Every time I feel like I understand it, something new comes up and proves me wrong. I have been given an example in my text and I did the question before looking at the answer. I don't understand why they did it the way they did and I feel like my answer is correct. Clearly I do not understand how to do this right. I was hoping someone could clear things up for me.
    My answer:
    f(x)=3^{x^2+1}-x^2\\f\prime(x)=3^{x^2+1}\cdot ln(3)\cdot 2x-(2x)
    text answer:
    f(x)=3^{x^2+1}-x^2\\f\prime(x)=(x^2+1)\prime3^{x^2+1}\cdot ln(3)-2x\\=(2x)3^{x^2+1}\cdot ln(3)-2x

    Also, the chain rule I have been given for exponential functions is this:
    f(x)=a^{g(x)} where a is a positive constant, is given by f\prime(x)=a^{g(x)} ln(a) g\prime(x), which I paired with the difference rule.


    So I guess what I'm really trying to figure out here, is why they put g\prime(x) in front?
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  2. #2
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    Re: More Chain Rule Help

    Quote Originally Posted by whit221 View Post
    Every time I feel like I understand it, something new comes up and proves me wrong. I have been given an example in my text and I did the question before looking at the answer. I don't understand why they did it the way they did and I feel like my answer is correct. Clearly I do not understand how to do this right. I was hoping someone could clear things up for me.
    My answer:
    f(x)=3^{x^2+1}-x^2\\f\prime(x)=3^{x^2+1}\cdot ln(3)\cdot 2x-(2x)
    text answer:
    f(x)=3^{x^2+1}-x^2\\f\prime(x)=(x^2+1)\prime3^{x^2+1}\cdot ln(3)-2x\\=(2x)3^{x^2+1}\cdot ln(3)-2x

    Also, the chain rule I have been given for exponential functions is this:
    f(x)=a^{g(x)} where a is a positive constant, is given by f\prime(x)=a^{g(x)} ln(a) g\prime(x), which I paired with the difference rule.


    So I guess what I'm really trying to figure out here, is why they put g\prime(x) in front?
    Your answer: $f\prime(x)= 3^{x^2+1}\cdot ln(3)\cdot 2x-(2x).$

    Book answer: $f\prime(x)= (2x)3^{x^2+1}\cdot ln(3)-2x.$

    Those two answers mean exactly the same thing: multiplication is commutative.
    Thanks from whit221
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  3. #3
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    Re: More Chain Rule Help

    I guess I was stressing over nothing. Thanks! ... just not sure why they needed to rearrange it.
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