ПОМОГИТЕ взять производную неявно заданной функции : [latex]x ln(y) = cos(xy^2)[/latex]

[latex]x ln(y) = cos(xy^2) \\\\ x'ln(y)+xln'(y)=cos'(xy^2) \\\\ ln(y)+x* \frac{1}{y} *y'=-sin(xy^2)*(xy^2)' \\\\ ln(y)+ \frac{x}{y} *y'=-sin(xy^2)*(x'y^2+x(y^2)') \\\\ ln(y)+ \frac{x}{y} *y'=-sin(xy^2)*(y^2+x*2y*y') \\\\ ln(y)+ \frac{x}{y} *y'=-y^2sin(xy^2)-2xysin(xy^2)*y' \\\\ \frac{x}{y} *y'+2xysin(xy^2)*y'=-y^2sin(xy^2)-ln(y) \\\\ ( \frac{x}{y}+2xysin(xy^2))*y'=-(y^2sin(xy^2)+ln(y)) \\\\ y'=- \dfrac{y^2sin(xy^2)+ln(y)}{ \frac{x}{y}+2xysin(xy^2)} [/latex]