Question

How do you find the derivative of `f(t)=(3^(2t))/t`?

Answer 1

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

Explanation:

`f'(t) = (t*d/dt(3^(2t))-3^(2t)*d/dt(t))/t^2` quotient rule
`f'(t) = (t*3^(2t)*ln(3)*d/dt(2t)-3^(2t)*1)/t^2` exponent differentiation, chain rule
`f'(t) = (t*3^(2t)*ln(3)*2-3^(2t))/t^2`
`f'(t) = (3^(2t)(2*ln(3)*t-1))/t^2`