Differentiate implicitly to find dydx secxy tanxy 11 7So

Differentiate implicitly to find dy/dx . sec(xy) + tan(xy) + 11 = 7

Solution

differentiate both sides with respect to x..

sec(xy)*tan(xy)[x*(dy/dx) + y] + sec² (xy)[x*(dy/dx) + y] + 0 = 0

sec(xy)*tan(xy)[x*(dy/dx) + y] + sec² (xy)[x*(dy/dx) + y] = 0

[sec(xy)*tan(xy)+ sec² (xy)][x*(dy/dx) + y] = 0

then if [x*(dy/dx) + y] = 0

then dy/dx = -y/x