Find dy/dx by implicit differentiation xy=6

dy/dx = -y/x

Step-by-step explanation:

xy = 6

x * dy  + y * dx = 0

Subtract y dx from each side

x dy = - y dx

Divide each side by dx

x dy /dx = -y dx/dx

x dy/dx = -y

Divide by x

dy/dx = -y/x

Step-by-step explanation:

Apply the derivative operator d/dx to xy = 6.  xy is a product, so we must use the product rule as well as the chain rule.

dy/dx = -y/x

(d/dx)(xy = 6)   works out to x(dy/dx) + y(dx/dx) = 0, or just x(dy/dx) + y = 0.

Solving this for dy/dx, we get, first, x(dy/dx) = -y, and then

dy/dx = -y/x

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

1. 34

2. 268

3. x=14.4

step-by-step explanation: