Calculus
posted by Aaron on .
d/dx[lnsquare root of(x^3) cube root of (x+3) fifth root of (3x2)]

are we taking ln of the whole thing??
I read it as
d( ln [ (x^3)^(1/2) (x+3)^(1/3) (3x2)^(1/5) ] /dx
let y = ln [ (x^3)^(1/2) (x+3)^(1/3) (3x2)^(1/5) ]
remember ln(AB) = lnA + lnB
so our
y = ln (x^3)^(1/2) + ln (x+3)^(1/3) + ln (3x2)^(1/5)
and remember ln A^n = n lnA
= 3(1/2) lnx + (1/3)ln(x+3) + (1/5)ln(3x2)
dy/dx = (3/2)(1/x) + (1/3)(1/(x+3) + 1/5)(3/(3x2))
= 3/(2x) + 1/(3(x+3)) + 3/(5(3x2))
I would not take it any further, it would look even messier, having to form a common denominator of
30(x+3)(3x2)