# Derivative of logarithmic functions

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- derivative of log with arbitrary base

$\frac{{d}}{{{d}x}}\;{\log _5}x$

$\frac{{d}}{{{d}x}}{\;log}\left( {1000 - \csc x} \right)$ - derivative of natural log

$\frac{{d}}{{{d}x}}{\;ln}x$

$\frac{{d}}{{{d}x}}{\;ln}\left( {\cos x} \right)$

$\frac{{d}}{{{d}x}}{\;ln}\left( {5{x^3} - 2x + 7} \right)$ - Differentiate:

$y = {^3}\sqrt{{{\;ln}x\;}}$