Posted by **NGOFAKA** on Tuesday, October 23, 2007 at 12:11pm.

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

- Maths -
**drwls**, Tuesday, October 23, 2007 at 12:49pm
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

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