Question

100 POINTS PLEASE SOLVE WITH STEPS. THANK YOU!!!

Answer 1

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