Wel a very basic doubt...............

When we differentiate a curve we get slope of the tangent not the equation of the tangent.

For example:
take y=2x+2

differentiating it we get "2" so 2 is slope of tangent not the equation of tangent.

take y=x²+4x+2

differentiating it we get 2x+4 but this is not the equation of tangent it is slope at any point (x,f(x))

so tangent at any point (x₀,x₀²+4x₀+2) is y=(2x₀+4)x+c
where c can be found by putting (x₀,x₀²+4x₀+2) in equation y=(2x₀+4)x+c..

hope its clear...