How do you find the derivative of $log_7x$ ?

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Answer 1 · 2016-01-03T16:42:47

Rewrite the expression using the change of base formula.

$log_7x=lnx/ln7$

This is simple to differentiate. The only tricky thing is to remember that $1/ln7$ is a constant, so it can be brought outside when differentiating:

$d/dx(lnx/ln7)=1/ln7*d/dx(lnx)$

Since $d/dx(lnx)=1/x$ ,

$d/dx(lnx/ln7)=1/ln7(1/x)=color(red)(1/(xln7)$

How do you find the derivative of log_7xlog_7x?