calculate the slope of tangent to the given function at the given point

Question

f(x) = 2 / √x+5 , P(4,2/3)

Answer 1

I assume you meant:
f(x) = 2/√(x+5) = 2(x+5)^(-1/2)

f ' (x) = -(x+5)^(-3/2)
at (4, 23)
f ' (4) = -(9)^(-3/2)
= -1/9^(3/2) = -1/27

tangent equation:
(y-2/3) = (-1/27)(x-4)
27y - 18 = -x + 4
x + 27y = 22