Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 65

You need to evaluate the equation of the tangent line at (-5,5), using the formula:
f(x) - f(-5) = f'(-5)(x + 5)
Notice that f(-5) = 5.
You need to evaluate f'(x), using the quotient rule, such that:
f'(x) =((x)'(x+4) - (x)(x+4)')/((x+4)^2)
f'(x) = (x+4 - x)/((x + 4)^2)
f'(x) = 4/((x+4)^2)
You need to evaluate the derivative at x = -5:
f'(-5) = 4/((-5+4)^2) =>< f'(-5) = 4
Replacing the values into equation yields:
f(x) - 5= 4(x + 5)
f(x) = 4x + 25
Hence, evaluating the equation of the tangent line at the given curve, yields f(x) = 4x + 25.