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))
