What is the derivative of #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)#