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Thread: exponential differentiation

  1. #1 exponential differentiation 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    hello, currently im studying the exponential and logarithmic differentiation and integration, and i came across this, and strangely enough i cant finish approaching it, though im on the right track, can anyone help me differentiate this please? thank you



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  3. #2 Re: exponential differentiation 
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    Quote Originally Posted by Heinsbergrelatz
    hello, currently im studying the exponential and logarithmic differentiation and integration, and i came across this, and strangely enough i cant finish approaching it, though im on the right track, can anyone help me differentiate this please? thank you

    use the chain rule


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  4. #3  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    yes i know you have to use the chain rule, after doing:


    but somehow, i cant get the correct answer..
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  5. #4  
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    you just need to differentiate to complete the chain.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  6. #5  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    but if we only differentiate that, we are completely ignoring the differentiating rule of the natural log function?
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  7. #6  
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    you need to differentiate that in conjunction with the differentiation of the natural log function. Remember, h(x)=(f(g(x)) : h'(x)=f'(g(x))g'(x)dx
    Wise men speak because they have something to say; Fools, because they have to say something.
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  8. #7  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    yes i remeber, but the rule in my book says,




    in general;
    where is a function of
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  9. #8  
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    it's the same thing as what I wrote. u is a function, in this case . now differentiate it.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  10. #9  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    but how about the ?
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  11. #10  
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    you have that, and you multiply it with to complete the chain rule. That's all. and for u, chances are the quotient rule would be a good place to start.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  12. #11  
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    Quote Originally Posted by Heinsbergrelatz
    yes i remeber, but the rule in my book says,




    in general;
    where is a function of
    the end products in the first two differentiations are missing a 'dx' at the end. That could be the source of some of your confusion.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  13. #12  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    ok i get the procedure now, thank you,

    o yes, by the way, does it matter in this case substantially without the "dx"?
    and also what does this "dx" denote exactly?
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  14. #13  
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    dx is, probably oversimplifying, the derivative of x, or rather, the change of x. In most cases it's useful when dealing with x's that are functions of other variables, as a reminder to take the derivative, using the chain rule, until you are down to the most isolated variable.
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  15. #14  
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    oh i see, well thank you for the help,i appreciate it
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