Hello tutors, can I please get your help regarding the following question. It uses points (1) through (18) as reference. Please let me know what you think, thank you.

Rules (12) - (18) essentially restate one of the rules (1) - (9) using the language of integrals instead of the language of derivatives. For example, (12) is essentially restating (3). Which rules are (13) - (18) restating?

Derivative Rules Recall the following derivative rules, where c is a real number and f and g are differentiable functions: Constant rule: a ( c ) = 0 d.x (1) Power rule for derivatives: d dx -(20 ) = cac-1 (2) Linearity of derivatives: do (f (2) + g(x)) = f'(x) + g'(x) and -(cf(x)) = cf'(x) (3) Product rule: d dx (f (z) . g(20) ) = f(2) . g'(2) + f'(2) . 9(2) (4) Quotient rule: d f(x) g(a) f' (a) - f(2)g' (2 ) dx g(x) 92 (2) (5) Chain rule: d dx (f (g(z))) = f'(9(2)) . 9' (20 ) (6) Trigonometric derivatives: d - sin(x) = cos(x) and a dx - cos(x) = - sin(x) (7) Exponential derivative: d r = ex dx (8 d Logarithmic derivative: dx In(a) = (9)Integral Rules An antiderivative or indefinite integral of a function f, written J f(x)dx, is a differentiable function F such that F'(x) = f(x) for any x in the domain of f. An antiderivative should always end with "+c", where c is understood to be an arbitrary real number; for example, f(1)dx = x + c, because any function of the form x + c, like x, x + 7, or x + (-100000), is an antiderivative of 1. We can now state the fundamental theorem of calculus, which we abbreviate FTC: FTC Part 1: Every continuous function has an antiderivative. (10)Letting a and b be real numbers, the definite integral of a function f from a to b, written Jo f(x)dx, is the area under the graph of f(x) between the x-values a and b. We will rely upon the following fact to calculate definite integrals: FTC Part 2: If F is an antiderivative of f, then J 's(a)da = F(b ) - F(a) . (11) The following are the integral rules you should know, where f and g are continuous functions and u and v are differentiable functions: Linearity of integrals: / (f(x) + 9(x))dx - / f(x)dx + / 9(x)da and af(x)dx = a / f(x)dx if a is a real number (12) Power rule for integrals: a+ +c if a is a real number with a # -1 (13) Special case of power rule for integrals: x 'dx = In la| + c (14) Trigonometric integrals: cos(x) da = sin(x) + c and sin(x)dx = - cos(x) + c (15) Exponential integral: / edx = ex + c (16) u-substitution: / f'(u(x))u'(x)da = f(u(x)) + c (17) Integration by parts: u(x)o'(x)dx = u(z)v(z) - v(x)u'(x)da (18) The last two rules here are by far the most difficult to apply; when we are using these two rules, a common convention is to use "du" as a shorthand for u'(x)dx, and "du" as a shorthand for v'(x) dx