What is the derivative of #log_4^(x^2)#?

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Answer 1 · 2015-07-18T00:25:31

Assuming you mean:

#y = log_4(x^2)#

rather than:

#log_4^(x^2)(x)# (why would you mean that??)

Change of Base law:
#y = (lnx^2)/(ln4)#

Now take the derivative:

#(dy)/(dx) = 1/ln4d/(dx)[lnx^2] = 1/ln4*1/(x^2)*2x#

#(dy)/(dx) = color(blue)(2/(xln4))#