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Math Help - proportionality of rate of change

  1. #1
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    proportionality of rate of change

    Doing another problem:

    Show that the rate of change of proportionality of rate of change-codecogseqn-12.gif is proportional to y.

    I know that you have to find the derivative & somehow find a constant to place in front of y. ​Stuck here.
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  2. #2
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    Re: proportionality of rate of change

    Quote Originally Posted by zachd77 View Post
    Doing another problem:

    Show that the rate of change of Click image for larger version. 

Name:	CodeCogsEqn-12.gif 
Views:	10 
Size:	468 Bytes 
ID:	26390 is proportional to y.

    I know that you have to find the derivative & somehow find a constant to place in front of y. ​Stuck here.
    what did you get for the derivative of y ?
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  3. #3
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    Re: proportionality of rate of change

    I got 3^(2x)*(7 ln(5))5^(7x)+5^(7x)*(2 ln(3))9^x... bit messy, best I could do to show y'
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  4. #4
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    Re: proportionality of rate of change

    y' = 3^{2x} \cdot 7\ln{5} \cdot 5^{7x} + 5^{7x} \cdot 2\ln{3} \cdot 3^{2x}

    y' = 3^{2x}5^{7x}(7\ln{5} + 2\ln{3})

    y' = y(7\ln{5} + 2\ln{3})
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  5. #5
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    Re: proportionality of rate of change

    thanks!!
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