Question

2x2-xy-y2=15 find dy ait (2,5) doc​

Answer 1

the answer is 1/4

Explanation:

using the implicit differentiation approach

dy/dx = (-4x+y)/(-x-2y)

dy/dx at point (2,5) =¼

Answer 2

1/4.

Explanation:

Using implicit differentiation:

2x^2 - xy - y^2 = 15

4x - (x.dy/dx +1.y) - 2y.dy/dx = 0

4x - x.dy/dx - y - 2y.dy/dx =0

-2y.dy/dx - x. dy/dx = y - 4x

dy/dx = (y - 4x)/(-2y - x).

So at the point (2, 5):

dy/dx = (5 - 4(2)) / (-2(5) - 2)

= -3/-12

= 1/4.