Question

find the equation of the tangent line to sin(x+y)=xy at (x,y)=(0,0)

Answer 1

first differentiate implicitly

Answer 2

cos(x + y)(1 + dy/dx) = x dy/dx + y

now find dy/dx in terms of x and y
then plug in x = 0 and y = 0 to get the slope of the tangent line.

Answer 3

so in term of X. the final result should be
y=cos(x+y)-y/x-cos(x+y)

Answer 4

@cwrw238

Answer 5

cos(x + y) + cos(x + y)dy/dx= x dy/dx + y
cos(x + y)dy/dx - x dy/dx = y - cos(x+y)
dy/dx = y - cos(x+y)
------------
cos(x + y) - x

x = 0 and y = 0

dy/dx = 0 - cos 0
-------- = -1
cos 0 - 0

so the slope of the tangent line is -1

y - y1 = m(x - x1)

x1 = y1 = 0 , m = -1

y = -x is the required tangent line