# Find the slope of the curve

## Homework Statement

At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as requested. x^6y^6=64, normal at (2,1)

## The Attempt at a Solution

64/y^6
or 6x6y=0, that's as far as I am getting, totally lost.

$$x^6 y^6 = 64$$
$$\frac{dy}{dx}:x^2y^2=4$$$$\frac{d}{dx} \left ( x^2y^2=4 \right )$$$$y^2\frac{d}{dx}x^2 + x^2\frac{d}{dx}y^2 = 0$$$$2xy^2 + 2yx^2\frac{dy}{dx} = 0$$$$\frac{dy}{dx} = \frac{-2xy^2}{2yx^2} = -xy$$