x-cot(xy)=6,求dy/dx

Question

x-cot(xy)=6,求dy/dx

Answer 1

let u = xy
(d/dx) [ x - cot (xy) ] = 0
1 - (d/dx) [ cot(xy) ] =0
1 = (d/du) [ cot u] * (d/dx) (u)
1 = [ -cosec^2 (xy) ] [ y + x (dy/dx) ]
1 / [ -cosec^2 (xy) ] = y + x (dy/dx)
dy/dx = [ y[ cosec^2 (xy)] +1 ] / { -x [ cosec^2 (xy) ] }