Question

differentiate
$y = log_{7}( logx )$

Answer 1

$y = log_{7}(logx) \\ \\ by \: using \: the \: property \: of \: log\\ y = \frac{ log_{e}log(x) }{ log_{e}(7) } \\ \\ on \: differentiating \: both \: sides \\ \\ \frac{dy}{dx} = \frac{d}{dx} (\frac{ log_{e}log(x) }{ log_{e}(7) }) \\ \\ since \: log_{e}(7) is \: a \: constant \: term \\ \frac{dy}{dx} = \frac{1}{{ log_{e}(7) }} \frac{d}{dx} (log_{e}logx) \\ \\ \frac{dy}{dx} = \frac{1}{{ log_{e}(7) }} \times \frac{1}{ log(x) } \times \frac{d}{dx} log(x) \\ \frac{dy}{dx} = \frac{1}{{ log_{e}(7) }} \times \frac{1}{ log(x) } \times \frac{1}{x} \\ \frac{dy}{dx} = \frac{1}{x log(7) log(x) }$


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