What is the first derivative of v(t)=(1+3^t)/3^t?

Given the function:

v(t) =
(1+3^t) /3^t

We need to find the first derivative
v'(t).

First we will rewrite the
fraction:

V(t) = 1/3^t  +
3^t/3^t

      = 3^-t  +
1

==> v(t) =(1/3^t) 
+1

Now we will
differentiate.

==> v'(t) = (1/3^t)' +
(1)'

               = (3^-t)' +
0

We will assume that u= -t ==> u' = -
1

==> v'(t) =
(3^u)'

==> v'(t) = 3^u * ln3 *
u'

               = 3^-t * ln3 *
-1

               = -ln3 /
3^t

But we know that -ln3 = ln3^-1 =
ln(1/3)

==> v'(t) = -ln(1/3) /
3^t