Question

Question #0ed82

Answer 1

`y'(5)=-16/5`

Explanation:

Making use of implicit differentiation and the product rule, we have

`d/dx(3x^2+3x+xy) = d/dx5`

`=> (d/dx3x^2)+(d/dx3x)+(d/dxxy) = 0`

`=> 6x + 3 + [x(d/dxy) + y(d/dxx)] = 0`

`=> 6x + 3 + xdy/dx + y = 0`

`=> dy/dx = -(6x+y+3)/x`

Evaluated at `x=5`, and noting that `x=5` implies `y=y(5) = -17`, we have

`y'(5) = dy/dx|_(x=5)`

`= -(6(5)+(-17)+3)/(5)`

`=-(30-17+3)/5`

`=-16/5`