# Thread: Rate of change

1. ## Rate of change

How do you do the following rate of change questions

when t = 1.2 for all the following questions:

1) y = 4/t + 4lnt

2) x = sin(t^2 +1) , y = cos(2t -3)

3) x = 1 / 1+2t , y = t / 1+t

4) q = 2e^-t/2.cos2t

5) x = e^2t.t^3(2-t)^4

Please could you explain the process as im quite lost. Thanks

2. e for 4) and 5) is the exponent

3. Originally Posted by dadon
How do you do the following rate of change questions

when t = 1.2 for all the following questions:

1) y = 4/t + 4lnt

2) x = sin(t^2 +1) , y = cos(2t -3)

3) x = 1 / 1+2t , y = t / 1+t

4) q = 2e^-t/2.cos2t

5) x = e^2t.t^3(2-t)^4

Please could you explain the process as im quite lost. Thanks
The rate of change is the derivative with respect to time. So for 1):

$
y = 4/t + 4 \ln(t)
$

so:

$
\frac{dy}{dt}=\frac{-4}{t^2} + \frac{4}{t}
$
,

so when $t=1.2$:

$
\frac{dy}{dt}=\frac{-4}{1.2^2} + \frac{4}{1.2}=0.5555..
$

RonL

4. ## Re:

Thanks! On that question (1) I was confused about the 4lnt part. You make it seem so simple!