`xy = 6, (-6,-1)` Find `dy/dx` by implicit differentiation and evaluate the derivative at the given point.

Expert Answers
mathace eNotes educator| Certified Educator

Given: `xy=6,(-6,-1)`

`xdy/dx+y=0`

`xdy/dx=-y`

`dy/dx=-y/x`

`dy/dx=-(-6)/(-1)`

`dy/dx=-6`

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kandukurimaths | Student

xy=6 at (-6,-1)

y=6/x

y=6x^(-1)

using d(x^n)/dx=nx^(n-1)

y=-6x^(-2)

y=-6/x^2  at (-6,1)

y=-6