Maths
posted by NGOFAKA .
if sqrt(y)=arctan(x), show that (1+x^2)dy/dx((1+x^2)dy/dx)=2

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
Similar Questions

calculus
Let f be a function defined by f(x)= arctan x/2 + arctan x. the value of f'(0) is? 
Complex numbers
For the transformation w=(z+i)/(zi) 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 … 
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 … 
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)=pi2arctan(b) b=sin(pi2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b)) sin(ab)=sinacosbcosasinb … 
Maths
if sqrt(y)=(arctan)tan1(x), show that (1+x^2)dy/dx((1+x^2)dy/dx)=2 
Calculus
1.Evaluate: (1/(x*sqrt(x^24)) I know the answer is 1/2*arctan(2/sqrt(x^24)), 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 … 
PreCalculus
I'm unsure how to even start this problem Solve for x: Arctan( 4/5 ) + Arcos (2/SQRT(5) ) = Arctan(x) 
Calc
Evaluate the integral (3x+4)/[(x^2+4)(3x)]dx a. (1/2)ln(x^2+4) + ln3x + C b. (1/2)arctan(x/2) + ln3x + C c. (1/2)arctan(x/2)  ln3x + C d. ln(sqrt(x^2+4)/(3x)) + C e. None of the above 
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) 
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?