Post a New Question

Calculus

posted by .

d/dx[lnsquare root of(x^3) cube root of (x+3) fifth root of (3x-2)]

  • Calculus -

    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)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Inter. Algebra

    Count Iblis how do you simplify 3square root sign with this underneath (3x squared y) to the third power?
  2. math

    What does it mean to have the sqaure root of 5 with a 2 in front of it?
  3. Math

    Simplify by taking roots of the numerator and the demoninator. Assume that all expressions under radicals represent positive numbers. The square root of 243x^6/y^20 to the fifth root. Here is what I have so far: the square root of …
  4. Calculus

    Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their domains. f(x)= square root of x, g(x)= cube root of 1-x These are my answers, but I am not sure about them and I only figured out one domain... that is the part that …
  5. Calc

    Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their domains. f(x)= square root of x, g(x)= cube root of 1-x These are my answers, but I am not sure about them and I only figured out one domain... that is the part that …
  6. Algebra

    Simplify: 5(cube root of 16) + 2(cube root of 54) 5 times the cube root of 16 plus 2 times the cube root of 54. I do not know how to type in the radical signs. Sorry.
  7. Algebra

    I need help on these kinds of radical problems. Once I get the examples solved, I think I can do others. 1. What is the solution to the square root of -9?
  8. Math PLEASE HELP ASAP

    -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT PLEASE. *CHALLENGE. 1.SIMPLIFY : SQUARE ROOT OF 16^8+8^4/16^2+16^7 2.EXPRESS 1 + 1/1+SQUARE ROOT OF 2 - 1/1-SQUARE ROOT OF 2 IN THE FORM A+B SQUARE ROOT OF 2, WHERE A AND BARE RATIONAL …
  9. college pre-calculus

    simplify: square root (4/3)-square root (3/4) A. 2-sqaure root(3)/2 square root (3) B. square root (7/12) C. square root (3)/6 D. 2/square root (3) which answer?
  10. maths surds please help and explain

    Simplify A.1/root a +2 b.root 18/25 c.root a x cubed root a d.root x + 2 root y/root x-2 root y e.root5 x root72 /root 3

More Similar Questions

Post a New Question