What you will need for the other three questions:

1. If g(x) = kx^j where k and j are constants,

g ‘ (x) = j*k*x^(j-1)

2. If g(x) = ke ^ f(b) where k is a constant and f(b) is a function,

g ‘ (x) = k* f ‘ (b) e ^ f(b)

3. If g(x) = k ln f(b) where k is a constant and f(b) is a function,

g'(x) = k * f ‘ (b) * 1 / f(b)

4. if g(x) = h(x) * j(x) where h(x) and j(x) are functions,

g ‘ (x) = h(x) * j ‘ (x) + h ‘ (x) * j(x)

This information is all you need to know to solve these problems. If you have any other questions, just edit your current question and I will check back tomorrow.

I will do one sample problem for you:

Problem 3: f(x) = 3x^(3) * e^(3x)

Step 1: Replace 3x^(3) with h(x) and e^(3x) with j(x)

h(x) = 3x^3

j(x) = e^(3x)

f(x) = h(x) * j(x)

Step 2: Find h ‘ (x) and j ‘ (x)

h ‘ (x) = 9x^2 Using RULE 1

j ‘ (x) = 3e^(3x) Using RULE 2

Step 3: Enter h(x), j(x), h ‘ (x), and j ‘ (x) into RULE 4’s equation.

f ‘ (x) = h(x) * j ‘ (x) + h ‘ (x) * j (x)

f ‘ (x) = 3x^3 * 3e^ (3x) + 9x^2 * e^(3x)

Step 4: Now that you have the equation for the slope of the line on any x, plug in x = 1 into your new equation

f ‘ (1) = 3 * 1^3 * 3e^(3*1) + 9 * 1^2 * e^(3*1)

Step 5: Simplify, and the result is your answer

f ‘ (1) = 18 e ^ 3