HELP CALCULUS

Find
dy/dx
by implicit differentiation.
tan−1(4x2y) = x + 3xy2

  1. 👍 0
  2. 👎 0
  3. 👁 3,730
  1. Just use the product and chain rules:

    arctan(4x^2y) = x + 3xy^2

    1/(1+16x^4y^2) * (8xy+4x^2y') = 1 + 3y^2 + 6xyy'

    8xy/(1+16x^4y^2) + 4x^2/(1+16x^4y^2) y' = 1+3y^2 + 6xyy'

    y'(4x^2/(1+16x^4y^2) - 6xy) = 1+3y^2 - 8xy/(1+16x^4y^2)

    At this point, it's just algebra, and serves no useful purpose to pursue it much further. Just solve for y' and you can massage it in various ways, as shown here:

    http://www.wolframalpha.com/input/?i=derivative+arctan%284x^2y%29+%3D+x+%2B+3xy^2

    1. 👍 1
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    Find y'' by implicit differentiation. 3x3 + 4y3 = 1

  2. Calculus [Implicit Differentiation]

    If √x+√y=10 and y(16)=36, find y'(16) by implicit differentiation. If somebody could please help me by explaining how to solve this problem ! Thank you (:

  3. Calc

    Find y'' by implicit differentiation. 5x2 + y2 = 3 y'' =?

  4. Calculus 1

    If 5x^2+5x+xy=2 and y(2)= -14 find y'(2) by implicit differentiation

  1. Calculus

    Use implicit differentiation to find dz/dy for yz = ln (x+z) I am unsure of how to deal with the right side specifically.

  2. Math

    use implicit differentiation to find the point where the parabola defined by x^2-2xy+y^2+4x-8y+20=0

  3. calculus

    Find the derivative of the function 1)f(t)=tan(e^2t)+e^tan2t f'(t)= [im not quite sure with this. im assuming the implicit differentiation] 2) F(t)=e^(8tsin2t) [for this one i got 2e^(8t)(4sin(2t)+cos(2t)) but it is incorrect.

  4. calculus 1

    Please help !!!!! Find dy/dx by implicit differentiation. (sin πx + cos πy)4 = 65

  1. Calculus

    Find dy/dx by implicit differentiation: x^2-2xy+y^3 = c Thank you!

  2. Math

    Find dy/dx by implicit differentiation. cot(y) = 4x − 6y

  3. calculus

    Find dy/dx by implicit differentiation. arctan(2x^2y)=x+4xy^2

  4. Calculus

    use implicit differentiation to find dy/dx if x^3+y^3=6xy

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