Answer:
y = -3π/2 x + π
Step-by-step explanation:
sin(xy) = ½
The slope of the tangent line is dy/dx. Take the derivative of both sides with respect to x. You'll need to use chain rule and product rule.
cos(xy) (x dy/dx + y) = 0
x dy/dx + y = 0
x dy/dx = -y
dy/dx = -y/x
At x = ⅓ and y = π/2:
dy/dx = -(π/2) / ⅓
dy/dx = -3π/2
Using point-slope form of a line:
y − π/2 = -3π/2 (x − ⅓)
Simplifying to slope-intercept form:
y − π/2 = -3π/2 x + π/2
y = -3π/2 x + π
