Derivative of y = 6(x)ln(x)-x+1? I haven't done any calculus in a year or so but think it's something to do with the chain rule. Not sure what to choose as the "inside" and "outside" parts though - any help very much appreciated.

Question

anonymous · Answer

If im interpreting your equation right its:

$$y=(6x)*ln(x)-x+1, \right?$$

if you use the chain rule and make ln(x) the inside function of $$U^V$$, where lnx=U and 6x=V, you risk getting something ugly such as ln(ln(x)) in your unsimplified answer, which is ugly.

try the product rule with the same assignments, U=lnx and V=x
U'=1/x and V'=6
so U'V+UV' = (1/x)6x+6lnx
in total we get 6lnx+6-1
or 6lnx+5

nikolas · Answer

Aha, of course it was the product rule I should have been using! Great explanation, thank you :)