Question #0ed82

1 Answer
Nov 19, 2016

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