Question

Find dy/dx for xy=4 at (-4,-1)

Answer 1

-
`(1)/(4)`

Explanation:

Differentiate implicitly using the product rule

x.
`(dy)/(dx)` + y.1 = 0 ( subtract y from both sides )

x .
`(dy)/(dx)` = - y ( divide both sides by x )

`(dy)/(dx)` = -
`(y)/(x)`

At (- 4, - 1), then

`(dy)/(dx)` = -
`(-1)/(-4)` = -
`(1)/(4)`