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

1 Answer
Alan N.
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#

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