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 (3x-2)]

- 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) (3x-2)^(1/5) ] /dx

let y = ln [ (x^3)^(1/2) (x+3)^(1/3) (3x-2)^(1/5) ]

remember ln(AB) = lnA + lnB

so our

y = ln (x^3)^(1/2) + ln (x+3)^(1/3) + ln (3x-2)^(1/5)

and remember ln A^n = n lnA

= 3(1/2) lnx + (1/3)ln(x+3) + (1/5)ln(3x-2)

dy/dx = (3/2)(1/x) + (1/3)(1/(x+3) + 1/5)(3/(3x-2))

= **3/(2x) + 1/(3(x+3)) + 3/(5(3x-2))**

I would not take it any further, it would look even messier, having to form a common denominator of

30(x+3)(3x-2)

## 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? ...
- Math PLEASE HELP ASAP - -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT ...
- college pre-calculus - simplify: square root (4/3)-square root (3/4) A. 2-...

More Related Questions