Calculus

Differentiate and simplify as much as possible.

Cube root(5z+6/-9z+3).

The answer should be y'=
(23(-9z+23)^2/3)/9(3z-1)^2(5z+6)^2/3)

So far, I'm stuck at y'=[23/3(5z+6)(3z+1)][((5z+6)^1/3)/((-9z+3)^1/3)]

  1. 0
asked by Mike
  1. if you let w be the fraction, then you have

    w^(1/3)

    which has derivative

    1/3 w^(-2/3) dw/dz

    Now just use the quotient rule on dw/dz, and you get

    69/(-9z+3)^2

    That gives you

    1/3 * ((5z+6)/(-9z+3))^(-2/3) * 69/(-9z+3)^2

    1 * (-9z+3)^(2/3) * 69
    ---------------------------------------
    3 * (5z+6)^(2/3) * (-9z+3)^2

    which you can see is the desired answer. I see a (3z+1) in your answer, which is already a typo. Try breaking it up into factors as I did, and you should see things cancel.

    posted by Steve
  2. using the quotient rule, by first line derivative is

    y' = (1/3)[(5z+6)/(3-9z)]^(-2/3) [ (5(3-9z) - (-9)(5z+6) ]/(3-9z)^2
    = (1/3)[(5z+6)/(3-9z)]^(-2/3) [ 69/(3-9z)^2 ]
    = 23 (3-9z)^(2/3) / (5z+6)^2/3 [ 1/(3-9z)^2 ]
    = not getting your answer

    let's try the product rule
    y = (5z+6)^(1/3) ( 3-9z)^(-1/3)

    y' = (5z+6)^(1/3) (-1/3)(3-9z)^(-4/3) (-9) + ( 3-9z)^(-1/3) (1/3)(5z+6)^(-2/3) (5)
    = (9/3)(5z+6)^(1/3) (3-9z)^(-4/3) + (5/3)(3-9z)^(-1/3) (5z+6)^(-2/3)
    = (1/3)(5z+6)^(-2/3) (3-9z)^(-4/3) [ 9(5z+6) + 5(3-9z)]
    = 23(5z+6)^(-2/3) (3-9z)^(-4/3)

    check through my steps

    posted by Reiny
  3. looks like Steve and I have the same answer

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. radical expressions

    how do u simplify radical expressions such as cubed root of 125t^6w^2 4 125 has a cube root of 5 t6 has a cube root of t2 so you are left iunder the radial w2
  2. calculus

    I have been asked to solve this two different ways. The first way is to use the chain rule and then simplify (which I have already done properly), and the second way is to simplify and then differentiate (not necessarily with the
  3. Inter. Algebra

    Count Iblis how do you simplify 3square root sign with this underneath (3x squared y) to the third power? "3 square root sign" probably means "cube root", in which case [(3 x^2y)^3]^(1/3) = 3 x^2 y The cube root of any quantity x
  4. 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.
  5. Math

    i see were u got that from but this 1 is confusing. 6 (index 3) square root of 36 times 2 (index 3)square root of 6 Please use the following for roots: sqrt cubroot etc. Those, with parenthesis, make the problem clear. 6 cube root
  6. 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
  7. Math

    I'm having trouble understanding when I am supposed to add absolute values when simplifying radicals. (It's cube root not square root) XER and YER because it's a cube root and you can take cube root of negatives and positives.
  8. 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
  9. 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
  10. Math To: Reiny

    This is one whole question: (12) (10xy^3) (3x^2y^2) (5x) (2y) I don't know how to do any of these: simplify sqaure root of 160000 simplify sqaure root of 0.04 simplify 3 * square root 81 simplify square root of 900 simplify square

More Similar Questions