What is the derivative of $y = {log}_{5} x$ $y=log_5x$ ?

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Answer 1 · 2015-12-25T02:06:34

$y'=1/(xln5)$

Rewrite using the change of base formula.

$y=lnx/ln5$

$y'=1/ln5d/dx[lnx]$

Recall that $1/ln5$ is a constant, so it can be moved outside of the derivative.

Also know the identity that $d/dx[lnx]=1/x$ .

$y'=1/ln5(1/x)$

$y'=1/(xln5)$

What is the derivative of y=log_5xy=log5xy=log_5x?