Implicit Differentiation

Question

if 4x² + 4x + xy = 5 and y(5) = -23, find y'(5) by implicit differentiation.

y'(5) = ?

Thus an equation of the tangent line to the graph at the point (5,-23) is

y = ?

Answer 1

4x² + 4x + xy = 5

8x + 4 + y + x(dy/dx) = 0

dy/dx = (-8x - 4 - y) / x

Slope of tangent line = (-40 - 4 + 23) / 5 = -21/5

Equation of tangent line: y + 23 = (-21/5)(x - 5)

Answer 2

y'(5)= -21/5=-4.2

tangent line through (5,-23) is

y=-21x/5 -2

or

21x +5y=-10