math

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Let
f(x) = (7^(x))* (log base 3 of(x))
f '(x) =

  • math -

    you just need to memorize a couple more formulas:

    you know that if
    f = e^x
    f' = e^x

    f = a^x
    f' = a^x ln(a)

    logbx = ln(x)/ln(b)

    f = logbx
    f' = 1/ln(b) * 1/x

    so, for f above,

    f' = 7^x ln7 log3x + 7^x * 1/xln3
    = 7^x ln7 lnx/ln3 + 7^x *1/xln3
    = 7^x/xln3 (x ln7 lnx + 1)

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