Question

Find the equation of the tangent to the curve sin(x+y)=xy at the origin.

Answer 1

differentiate implicitly

cos(x+y) (1 + dy/dx) = x dy/dx + y
at (0,0_
cos(0)(1+dy/dx) = 0+0
1(1+dy/dx) = 0
dy/dx = -1

so slope is -1 , and y-intercept is 0

equation of tangent: y = -x

Answer 2

Thank you!!!