Posted by Aaron on Saturday, December 1, 2012 at 9:49am.
d/dx[lnsquare root of(x^3) cube root of (x+3) fifth root of (3x2)]

Calculus  Reiny, Saturday, December 1, 2012 at 10:48am
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)
Answer This Question
Related Questions
 Calculus  Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their ...
 Math  Simplify by taking roots of the numerator and the demoninator. Assume ...
 Calc  Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their ...
 maths surds please help and explain  Simplify A.1/root a +2 b.root 18/25 c.root...
 Algebra  Simplify: 5(cube root of 16) + 2(cube root of 54) 5 times the cube ...
 Inter. Algebra  Count Iblis how do you simplify 3square root sign with this ...
 Algebra  I need help on these kinds of radical problems. Once I get the ...
 math  What does it mean to have the sqaure root of 5 with a 2 in front of it? ...
 college precalculus  simplify: square root (4/3)square root (3/4) A. 2sqaure...
 Math PLEASE HELP ASAP  PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT ...
More Related Questions