How do you find the derivative of #logx^2#?

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Answer 1 · 2016-01-10T00:40:22

#2/(xln10)#

Use logarithm rules to rewrite the function as

#2logx#

Also, recall that #logx=log_10x#, and apply the change of base formula to the logarithm to put it into a form containing the natural logarithm.

#2(lnx/ln10)#

If we want to differentiate this, remove the core function, #lnx#, from the constant it's being multiplied by.

#2/ln10*lnx#

Finding the derivative:

#2/ln10*d/dx[lnx]#

#2/ln10*1/x#

#2/(xln10)#