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.
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.
$\displaystyle xy = tan(xy)$
$\displaystyle xy' + y = sec^2(xy)(xy' + y)$ // chain rule
$\displaystyle xy' + y = sec^2(xy)xy' + sec^2(xy)y$ // expand
$\displaystyle xy' - sec^2(xy)xy' = sec^2(xy)y - y$ // move terms to opposite sides
$\displaystyle y'(1 - sec^2(xy)) = sec^2(xy)y - y$ // factor out y'
$\displaystyle y' = \frac {sec^2(xy)y - y}{1 - sec^2(xy)}$ // divide