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100 POINTS
PLEASE SOLVE WITH STEPS.

THANK YOU!!!

100 POINTS PLEASE SOLVE WITH STEPS. THANK YOU!!!-example-1
User Nocklas
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6.7k points

1 Answer

1 vote

Answer:

y = -3π/2 x + π

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

User Nikita Malyavin
by
6.4k points