#d/(dx)(logx/x^2)#

This will require the quotient rule, the power rule, and knowing the derivitave of #logx#.

Recall the quotient rule for finding a derivative:

#d/(dx)((P(x))/(Q(x)))=((Q(x)*P'(x))-(P(x)*Q'(x)))/(Q(x)^2)#

Or simply, #(BT'-TB')/B^2# where #T# is the top function and #B# is the bottom function.

Also recall that #d/(dx)log_a(x)=1/(xln(a))# where #a# is the base of the logarithm and #x# is the argument. You won't use this very often but you just need to memorize this.

Let's proceed:

#d/(dx)(logx/x^2)#

#=((x^2*1/(xln(10)))-(logx*2x))/(x^2)^2#

#=(x^2/(xln(10))-2xlogx)/x^4#

#=x^2/(x^4*xln(10))-(2xlogx)/x^4#

#=1/(x^3ln(10))-(2logx)/x^3#

Or

#=(1-2logxln(10))/(x^3ln(10))#