Find an equation of the tangent line to the curve at the given point.?

Question

y= 6x / (x+1)^2 at point (0,0)

Answer 1

f `(x) = [ (x + 1)² (6) - (6x)(2)(x + 1) ] / (x + 1)^4
f `(x) = [ 6 (x + 1) { (x + 1) - 2 x } ] / (x + 1)^4
f `(x) = [ 6 (x + 1) (1 - x) ] / (x + 1)^4
f `(0) = 6 / 1 = 6
f (0) = 0
y = 6 x is required equation.

Answer 2

the derivative of a function evaluated at a point gives the slope of the tangent at that point

so to solve this problem, find this slope. then you will have a point and slope from which you can generate the equation of the line.