how would i go about finding the differentiate of:

f(t) = 2-(2/3)t

i know the power rule and all that but i just dont know where to start....

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- Feb 8th 2010, 07:36 PMrhcp1231Help with differentiate functions
how would i go about finding the differentiate of:

*f*(*t*) = 2-(2/3)*t*

i know the power rule and all that but i just dont know where to start.... - Feb 8th 2010, 07:46 PMdedust
let $\displaystyle y = \left(\frac{2}{3}\right)^t$, then

$\displaystyle \ln y = t \ln \left(\frac{2}{3}\right)$

differentiate both side with respect to t

$\displaystyle \frac{1}{y} \frac{dy}{dt} = \ln \left(\frac{2}{3}\right)$

or

$\displaystyle \frac{dy}{dt} = y \ln \left(\frac{2}{3}\right) = \left(\frac{2}{3}\right)^t \ln \left(\frac{2}{3}\right)$

now,..solve your problem - Feb 8th 2010, 07:49 PMrhcp1231
my teacher didnt say anything about using natural logs to find the differentiate though