Question

Find f'(a) when f(t) = 2t+1/t+3

Answer 1

Are you dividing 2t+1 by t alone or by t+3? If by t+3, you must enclose (t+3) inside parentheses:

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

If this is the correct function, then decide what kind of function it is, so that you can choose the correct rule of differentiation. It's a QUOTIENT.

Please look up, jot down and then follow the Quotient Rule.
The numerator here is (2t+1), and the denominator is (t+3).

Answer 2

I'm assuming you mean (2t+1)/(t+3). using quotient rule, we get (2(t+3)-(2t+1))/(t+3) which is equal to -5/(t+3)^2