How to Find the Derivative of f(t) with Respect to t

[Namo]

f(t) = K(t) - K(t-T)

I want to find \frac{df}{dt}

i'm unsure of the notation, does the 3rd term represent K as a function of t-T :facepalm:? I know the 2nd term is showing K is a function of time otherwise it would be written simply Kt, but unsure of the 3rd term. I'm confused :S

If the 3rd term was a function of t-T shouldn't you call it a different function? In which case this equation means f(t) = K(t) - tK(t) + TK(t)

What would you say?

I believe the answer is

\frac{df}{dt} = \frac{dK}{dt} - K(t) - t\frac{dK}{dt} + T\frac{dK}{dt}

 

[epenguin]

It could be anything but seeing that you would expect T to represent a constant. You would expect it to be used when t is time. Then your formula would represent the difference between K at time t and at an earlier time (t - T).

df/dt = K'(t) - K'(t -T). In other words it's the difference between K' at time t and at an earlier time. That's all you can say about it* unless you have an explicit formula for the particular f, then you might be able to combine into something else.

Just draw some graphs of any functions and you should see.

*Well you could say that as T gets small it approaches f''(t).(t-T) .