posted by .

find y' if arctan(xy)=6+x^(4)y


    here is one way:

    xy = tan(6 + x^4y)
    xdy/dx + y = sec^2 (6 + x^4y) (x^4 dy/dx + 4x^3y_
    = x^4 dy/dx sec^2 (6+x^4y) + 4x^3y sec^2(6+x^4y)

    dy/dx(x - x^4sec^2 (6+x^4y) ) = 4x^3 sec^2 (6+x^4y) - y

    dy/dx = (4x^3 sec^2 (6+x^4y) - y)/(x - x^4sec^2 (6+x^4y) )

    check my algebra, I should have written it out on paper first.


    Or, more directly,

    1/(1+x^2y^2) (y+xy') = 4x^3y+x^4y'
    y+xy' = 4x^3y (1+x^2y^2) + x^4(1+x^2y^2)y'
    y' = (4x^3y + 4x^5y^3-y)/(x-x^4-x^6y^2)

    This can also be obtained (after restoring the y that was accidentally dropped) from Reiny's result by recalling the sec^2 = 1+tan^2 = 1+x^2y^2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Note that pi lim arctan(x ) = ---- x -> +oo 2 Now evaluate / pi \ lim |arctan(x ) - -----| x x -> +oo \ 2 / I'm not exactly sure how to attempt it. I have tried h'opital's rule but I don't believe you can use it here. Any help …
  2. calculus

    Let f be a function defined by f(x)= arctan x/2 + arctan x. the value of f'(0) is?
  3. calculus

    Find the exact value of: cos(arctan(2) + arctan(3)) Please explain how you got your answer. I have the answer, but I don't know how to get to it.
  4. Math

    Arrange these in order from least to greatest: arctan(-sqrt3), arctan 0, arctan(1/2) So far I got the first two values, arctan(-sqrt3), and that's 150 degrees. Arctan 0 would be zero degrees. I'll use just one answer for now, but I …
  5. calculus

    Now we prove Machin's formula using the tangent addition formula: tan(A+B)= tanA+tanB/1-tanAtanB. If A= arctan(120/119) and B= -arctan(1/239), how do you show that arctan(120/119)-arctan(1/239)=arctan1?
  6. Trig

    URGENT, Please answer this question: give the value of: Tan(Arctan x+1/x-1+Arctan x-1/x)
  7. calculus

    h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ?
  8. calculus

    h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ?
  9. calculus

    For x>0 find and simplify the derivative of f(x)= arctan(x) + arctan(1/x). I've done the problem a few times and I keep getting (1)/(1+(x)^2)+(1)/(1+(1/(1/x)^2))(-x)^-2 but something about the answer is wrong and I cannot figure …
  10. precal

    The values of x that are solutions to the equation cos^(2)x=sin2x in the interval [0, pi] are a. arctan(1/2) only b. arctan(1/2) and pi c. arctan(1/2) and 0 d. arctan(1/2) and (pi/2) e. arctan(1/2), o, and (pi/2)

More Similar Questions