`f(t)=(2t+1)/(t+3)`

The derivative of this function with respect to t can determined using the definition of derivative which is:

`f'(t)=lim_(h->0) (f(t+h)-f(t))/h`

To apply this formula, evaluate the given function at t=t+h to get f(t+h).

`f(t)=(2t+1)/(t+3)`

`f(t+h)=(2(t+h)+1)/((t+h)+3)`

`f(t+h)=(2t+2h+1)/(t+h+3)`

Then, plug-in this to the formula of above.

`f'(t)=lim_(h->0)((2t+2h+1)/(t+h+3)-(2t+1)/(t+3))/h`

Before taking the limit,...

(The entire section contains 273 words.)

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