What is the derivative of (3^(2t))/t?

1 Answer
Sep 24, 2016

f'(t) = ((2ln3*t-1)*3^(2t))/t^2

Explanation:

f(t)=3^(2t)/t = 3^(2t)*t^-1

ln f(t) = 2t*ln3-lnt

Using implicit differentiation:
1/f(t)*f'(t) = 2t*0 + 2*ln3 -1/t (Product rule and standard differential)

1/f(t)*f'(t) = 2ln3-1/t

Since f(t)=3^(2t)/t
f'(t) = 3^(2t)/t * (2ln3-1/t)

= = ((2ln3*t-1)*3^(2t))/t^2