Find f '(a). f(t) = 6t + 6/ t + 9

Question

f(t) = 6t + 6/ t + 9

f'(a)=______

Answer 1

For f(t) equal to (6t+6)/(t+9), f'(t) is given by [(t+9) times derivative of (6t+6) minus (6t+6) times derivative of (t+9)] divided by square of (t+9).

That is, f'(t) = [(t+9)(6) − (6t+6)(1)] ÷ (t+9)² which simplifies to [6t + 54 − 6t − 6]/(t+9)² or 48/(t+9)².

Then f'(a) is equal to 48/(a+9)².