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

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

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Answer 1 · 2017-12-18T01:18:36

#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#

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

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