# Math Preliminaries

This section briefly covers the mathematical tools we will use throughout this course. If you can do all the example problems easily, you should be ok skipping this section. If not, watch on.

## Part 1. Exponents

Exponents Examples

Simplify the following expressions:

• $\frac{x^3}{x} =$
• $(x^n)^\pi =$
• $\frac{x^{1/2}}{x} =$

Try these example problems on your own to check your understanding and then watch the video for a walk-through of the answers.

## Part 2. Derivatives

Derivatives Examples

Find the derivatives of the following expressions:

• $f(x)=3x^2$
• $f(x)=x2−10x+4$
• $f(x)=x^{1/2}$
• $f(x)=\ln⁡(1+x^2)$

Try these example problems on your own to check your understanding and then watch the video for a walk-through of the answers.

## Part 3. Partial Derivatives

Basic Partial Derivatives Examples

Find all partial derivatives of the following expressions:

• $f(x,y)=3yx^2$
• $f(x,y)=x^{1/3} y^{2/3}$
• $f(x,y)=10\ln{⁡}x+5\ln{⁡y}$

Try these example problems on your own to check your understanding and then watch the video for a walk-through of the answers.

Find all partial derivatives of the following expressions:

• $f(x,y)=(2x^2+3y)(4x+58y^2)$
• $f(x,y)=\ln{(1+yx^2)}$

Try these example problems on your own to check your understanding and then watch the video for a walk-through of the answers.

## Part 4. Solving for unknown variables

Solve for x Example

Solve the following expressions for $x$:

• $x−\frac{29\sqrt{\ln ⁡z}}{y}=0$
• $x^2−y=0$

Try these example problems on your own to check your understanding and then watch the video for a walk-through of the answers.

Note: the following video has an error at minute marker 2:38. It should say $y = 1$, and therefore $x = 1$.

Solving a system of equations example

Solve the following expression for $x$, $y$, and $z$:

• $\frac{x}{y} = z$
• $\frac{y}{x} = z$
• $2x + 4z = 10$

Use both approaches discussed above to check your understanding and then watch the video for a walk-through of the answers.

Did you feel like any of the videos above were confusing, or could use more detail? If you're a student at Iowa State University, send me a quick note at mclancy@iastate.edu, referencing the video number and your issue, if applicable.