Can someone check my answers please? (differentiation)

Question is find dy/dx of xy-sin(xy^2)=Pi/4+ 2^-1/2 when x=Pi/4 and y=1.

I differentiated implicitly to get

x(dy/dx) + y + cos(xy^2) * (y^2 +2xy dy/dx) = 0
x(dy/dx) + y + y^2cos(xy^2) + 2xycos(xy^2)dy/dx = 0
(x + 2xycos(xy^2))dy/dx = -y - y^2cos(xy^2)
dy/dx = (-y -y^2cos(xy^2))/(x + 2xycos(xy^2))

Subbing in values for x and y, i got:

dy/dx = (-1 -cos(Pi/4))/(Pi/4 + 2Pi/4cos(Pi/4))
dy/dx = (-1 - 1/2root2)/(Pi/4 + Pi/2 * 1/2root2)

Times top and bottom by 4root2 to give:



dy/dx = (-4root2 - 2)/(Piroot2 + Pi)

Couldn't get it any simpler than that, question doesn't state whether or not to leave in exact form so i was gonna put that into a calculator as well.

Can anyone confirm/correct my working?
Thanks in advance

Differenmtiation looks o.k. but in the evaluation note vthat $\frac{1}{2}\sqrt2\times 4\sqrt 2=4 \ NOT \ 2.$

Question is find dy/dx of xy-sin(xy^2)=Pi/4+ 2^-1/2 when x=Pi/4 and y=1.