# Math Help - proportionality of rate of change

1. ## proportionality of rate of change

Doing another problem:

Show that the rate of change of 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.

2. ## Re: proportionality of rate of change

Originally Posted by zachd77
Doing another problem:

Show that the rate of change of 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 ?

3. ## 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'

4. ## Re: proportionality of rate of change

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

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

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

thanks!!