log_{7 }(5 – 3x) Find the derivative​

Question

log_{7 }(5 – 3x)
Find the derivative​

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Acacia 4 years 2021-07-29T02:34:54+00:00 1 Answers 9 views 0

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  1. mit
    0
    2021-07-29T02:36:35+00:00
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    Let y be the expression you want to differentiate:

    y=\log_7(5-3x) \implies 7^y=5-3x

    Now,

    7^y=e^{\ln(7^y)}=e^{y\ln(7)}

    Use the chain rule to differentiate both sides with respect to x :

    \ln(7)e^{y\ln(7)}\dfrac{\mathrm dy}{\mathrm dx}=-3

    Solve for dy/dx :

    \ln(7)7^y\dfrac{\mathrm dy}{\mathrm dx}=-3

    \dfrac{\mathrm dy}{\mathrm dx}=-\dfrac3{\ln(7)7^y}

    \dfrac{\mathrm dy}{\mathrm dx}=\boxed{-\dfrac3{\ln(7)(5-3x)}}

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