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Math Help - derivative help plz

  1. #1
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    derivative help plz

    cant work out how to use the math tag

    need to find the derivative of (3+5t)^4t

    i got

    20(3+5t)^4t is that right if not need some help plz
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  2. #2
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    Hello, helmszee!

    We need logarithmic differentiation . . .


    Differentiate: . y \:=\:(3+5t)^{4t}

    Take logs: . \ln y \;=\;\ln(3+5t)^{4t} \;=\;4t\cdot\ln(3+5t)

    Differentiate implicitly: . \frac{1}{y}\cdot\frac{dy}{dt} \;=\;4t\cdot\frac{1}{3+5t}\cdot5 + 4\cdot \ln(3+5t) \;=\;\frac{20t}{3+5t} + 4\ln(3+5t)

    Multiply by y\!:\;\;\frac{dy}{dt}\;=\;y\left[\frac{20t}{3+5t} + 4\ln(3+5t)\right]

    Replace y\!:\;\;\frac{dy}{dt}\;=\;(3+5t)^{4t}\left[\frac{20t}{3+5t} + 4\ln(3+5t)\right]
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  3. #3
    Math Engineering Student
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    Quote Originally Posted by helmszee View Post
    need to find the derivative of (3+5t)^4t
    You can also apply the famous trick a=e^{\ln a},\,\forall a>0
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