Question

Find dy/dx at x=1 and y=pi/4 if sin^2 y + cos xy =k

Answer 1

We have to differentiate it

The question is sin^2 y +cos x =k

differentiate with respect to x on both sides

(2 sin y cos y )dy/dx +( - sin xy )*(y+dy/dx)=0

where k is constant

dy/dx =sin xy^2/(sin 2y - sin xy)

Now at x=1 and y=pi/4

dy/dx= sin (pi^2/16)/(1-1/√2)

=0.010/(√2-1)/√2

=0.010/(0.414)/√2