Find dy/dx in terms of x and y for:xy = tan(xy)

I'm not too good with this so pls dont skip steps pls.

Printable View

- Apr 25th 2009, 07:28 AMkangarooFind dy/dx in terms of x and y
Find dy/dx in terms of x and y for:

**xy = tan(xy)**

I'm not too good with this so pls dont skip steps pls. - Apr 25th 2009, 08:15 AMkangaroo
anyways, i've gotten this far and need help

xy=tan(xy)

d(xy)/dx = d(tanxy)/dx

x * dy/dx +y * dx/dx = sec^2(xy) * (d(xy)/dx)

1 = sec^2(xy)

1 = 1/(cos^2(xy))

cos^2(xy) = 1 - Apr 25th 2009, 08:24 AMderfleurer

// chain rule

// expand

// move terms to opposite sides

// factor out y'

// divide - Apr 25th 2009, 09:09 AMkangaroo
thanks!

btw, x has been left out of the factorizing line.

which when corrected, and factorised again after dividing, renders y' = -y/x

thanks again!!