Maths

posted by .

if sqrt(y)=arctan(x), show that (1+x^2)dy/dx((1+x^2)dy/dx)=2

  • Maths -

    If

    sqrt(y)=arctan(x),

    that means
    y = [arctan(x)]^2

    Let u = arctan x and use the chain rule

    y = u^2
    dy/dx = d(u^2)/du * du/dx
    = 2 arctan(x)/(1 + x^2)
    or
    (1 + x^2)*dy/dx = 2 arctan x = 2 sqrt y

    Are you sure you wrote
    (1+x^2)dy/dx((1+x^2)dy/dx)=2 correctly?
    That has (1+x^2)dy/dx appearing twice in a row. It doesnt look right

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

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

    For the transformation w=(z+i)/(z-i) show that as z moves along the real axis, w moves along a circle centre O and radius 1 I do not know where to start changing it to polar form will help w=magnitude @ (arctan 1/z - arctan -1/z) where …
  3. Math Help please!!

    Could someone show me how to solve these problems step by step.... I am confused on how to fully break this down to simpliest terms sqrt 3 * sqrt 15= sqrt 6 * sqrt 8 = sqrt 20 * sqrt 5 = since both terms are sqrt , you can combine …
  4. Trigonometry

    I need help with I just can't seem to get anywhere. this is as far as I have got: Solve for b arcsin(b)+ 2arctan(b)=pi arcsin(b)=pi-2arctan(b) b=sin(pi-2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b)) sin(a-b)=sinacosb-cosasinb …
  5. Maths

    if sqrt(y)=(arctan)tan-1(x), show that (1+x^2)dy/dx((1+x^2)dy/dx)=2
  6. Calculus

    1.Evaluate: (1/(x*sqrt(x^2-4)) I know the answer is -1/2*arctan(2/sqrt(x^2-4)), but I am having trouble getting to this answer on my own. I know the formula to solve it is 1/a*arctan(x/a) and that a=2, but that's all I know. 2.Find …
  7. PreCalculus

    I'm unsure how to even start this problem Solve for x: Arctan( -4/5 ) + Arcos (2/SQRT(5) ) = Arctan(x)
  8. Calc

    Evaluate the integral (3x+4)/[(x^2+4)(3-x)]dx a. (1/2)ln(x^2+4) + ln|3-x| + C b. (1/2)arctan(x/2) + ln|3-x| + C c. (1/2)arctan(x/2) - ln|3-x| + C d. ln|(sqrt(x^2+4)/(3-x))| + C e. None of the above
  9. 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)
  10. TRIGONOMETRY

    Evaluate the expressions: a) arctan(-sqrt(3)) a) Arctan(-sqrt(3)) So, I know how to find the answers with a calculator, but how do I find it step by step?

More Similar Questions