Derivative of logarithmic functions

Lessons

1. derivative of log with arbitrary base
   $\frac{{d}}{{{d}x}}\;{\log _5}x$
   $\frac{{d}}{{{d}x}}{\;log}\left( {1000 - \csc x} \right)$
2. derivative of natural log
   $\frac{{d}}{{{d}x}}{\;ln}x$
   $\frac{{d}}{{{d}x}}{\;ln}\left( {\cos x} \right)$
   $\frac{{d}}{{{d}x}}{\;ln}\left( {5{x^3} - 2x + 7} \right)$
3. Differentiate:
   $y = {^3}\sqrt{{{\;ln}x\;}}$