math problem??

Question

if (x^2)[(ln^2)(x)], then what does y'=?

i'm especially confused with the ln squared...how do you multiply with that?

Answer 1

[(ln^2)(x)] is basically (lnx)^2... it's just we prefer to write it in the way the question writes it as... so... to find the 1st derivative, we can use the product rule and chain rules
f[x]= x^2
f'[x]= 2x
g[x]= (lnx)^2
g'[x] = 2lnx * 1/x

Using the product rule:
=f'[x]g[x] + f[x]g'[x]
=(2x)([lnx]^2 + (x^2)(2lnx *1/x) is your answer