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    4. how to get the derivative of a quotient 3/(t+1)?
    how to get the derivative of a quotient 3/(t+1)?

    how to get the derivative of a quotient 3/(t+1)?

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    +1  Views: 401 Answers: 1 Posted: 13 years ago
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      1 Answer

      We'll differentiate the given function, with respect to t.


      We'll use the quotient rule:


      v'(t) = [(1+3^t)'*(3^t) - (1+3^t)*(3^t)']/(3^t)^2


      We'll differentiate and we'll get:


      v'(t) = [(3^t*ln3)*(3^t) - (3^t*ln3)*(1+3^t)]/(3^t)^2


      v'(t) = [(3^t*ln3)*(3^t - 1 -3^t)]/(3^t)^2


      We'll eliminate like terms from numerator:


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


      We'll simplify and we'll get:


      v'(t) = -(ln3)/(3^t)


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


      The first derivative of v(t)=(1+3^t)/3^t is:


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

      13 years ago. Rating: 1
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