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

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

    +1  Views: 400 Answers: 1 Posted: 13 years ago

    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)



    Top contributors in Mathematics category

     
    ROMOS
    Answers: 313 / Questions: 0
    Karma: 13510
     
    Colleen
    Answers: 367 / Questions: 0
    Karma: 6890
     
    country bumpkin
    Answers: 96 / Questions: 0
    Karma: 6240
     
    Bob/PKB
    Answers: 220 / Questions: 2
    Karma: 5030
    > Top contributors chart

    Unanswered Questions

    KKKJILI PH
    Answers: 0 Views: 2 Rating: 0
    KKKJILI PH
    Answers: 0 Views: 1 Rating: 0
    88vinnetpro
    Answers: 0 Views: 5 Rating: 0
    Cardilite Thailand
    Answers: 0 Views: 8 Rating: 0
    Ga Nuong Ngoc Lan
    Answers: 0 Views: 9 Rating: 0
    gavitex llc
    Answers: 0 Views: 8 Rating: 0
    > More questions...
    483863
    questions
    724168
    answers
    813342
    users