Question

Find the slope of the tangent line to the curve

−1/x²−3xy−1/y³=84.
a)−1
b)0
c)1
d)Undefined
​

Answer 1

To find the slope of the tangent line to the given curve, we need to take the derivative of the equation and solve for y'.

Step-by-step explanation:

To find the slope of the tangent line to the curve, we first need to take the derivative of the given equation. Differentiating both sides of the equation with respect to x, we get:

-(-2/x^3 - 3y - 3xy' - 3/y^4y') = 0

Simplifying the equation, we can solve for y':

y' = (2/x^3 + 3y^5) / (3x + 1/y^4)

Therefore, the slope of the tangent line to the curve is given by y'.