Derivative of 5logx, differentiate a base 10 log, derivative with non-standard base. #shorts

Derivative of 5logx, differentiate a base 10 log, derivative with non-standard base.

We differentiate 5logx by using the standard formula for the derivative of a logarithm with non-standard base. The 5 out in front is a spectator, and the derivative of log base-10 gives 1/x in addition to a factor of 1/ln(10). We clean up the answer, and we're done!