# Help with differentiate functions

• Feb 8th 2010, 08:36 PM
rhcp1231
Help 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, 08:46 PM
dedust
Quote:

Originally Posted by rhcp1231
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....

let $y = \left(\frac{2}{3}\right)^t$, then

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

differentiate both side with respect to t

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

or

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