math

Express y=[4x-x^3]/[3x^2+2)^2 as a product and then differentiate. Simplify your answer using positive exponents. Help Please! ty

  1. 👍 0
  2. 👎 0
  3. 👁 186
  1. y = (4x - x^3)(3x^2 + 2)^-2

    dy/dx = (4x - x^3)(-2)(3x^2+2)^-3(6x) + (3x^2+2)^-2 (4-3x^2)
    = (3x^2+2)^-3 [ -12x(4-x^3) + (3x^2+2)(4-3x^2)]
    = (3x^2 + 2)^-3 (3x^4 + 6x^2 - 48x + 8)
    = (3x^4 + 6x^2 - 48x + 8)/(3x^2 + 2)^3

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Please check answers)

    Perform the indicated operations and simplify the result. Leave your answer in factored form. 1) x/16 - 1/x all over 1 + 4/x A) x+4/16 B) x-4/16 C) 16/x+4 D) 16/x-4 E) -16/x+4 I chose answer C. I saw this as x^2-16/ x+4. Multiply

  2. Math(Please help)

    Simplify each expression. Assume all variables are positive. 1) 3 sqrt2 - 8 sqrt128 I think you subtract the 3 from the 8 but I do not know what else to do. 2) Simplify expression. Answer should have only positive exponents. (8x^3

  3. Alegbra

    Use properties of exponents to simplify the given expression. First express the answer in exponential form. Then evaluate the expression. 3^2 3^3=

  4. Algebra

    Simplify the expression. Assume that all variables represent positive numbers. Write your answer without using negative exponents. (343x^-6y/8y^-8x^6)^-2/3

  1. algebra

    Simplify write with positive exponents (-27y^9)1/3

  2. math

    Simplify. Your answer should contain only positive exponents. (when a number is between *__* its an exponent) 5y*-5* - ------- -u*5* v*-4* .(times) -uv*5* sorry if this is a bit confusing (hard to write this on a computer)

  3. calculus

    Find the derivative of the given function. Simplify and express the answer using positive exponents only. y= ((9x^2-4)^3/7x^2+4)

  4. math

    How do u simplify . Express final answer using positive exponents. 2^3= (B^4)^-3=

  1. algebra

    Simplify using only positive exponents. (2r^-1s^2t^0)^-2 ---------------- 2rs Thanks in advance! Working this out: (2^-2 r^2 s^-4)/ (2 r s) = r^2/8rs^5 Note: Anything to the 0 power is equal to 1. I hope this will help. Sorry but

  2. Math

    Simplify the following. Write your answer using positive exponents only: ( 5 c − 3 v 5 y − 8 )

  3. Applied Calculus......

    Rewrite the expression using positive exponents only. (Simplify your answer completely.) (x^3-y^3)(x^-3+y^-3)

  4. Math

    Short answer: simplify the following expression,and rewrite it in an equivalent form with positive exponents. (9x^-3)^3

You can view more similar questions or ask a new question.