# Ch 10: Calculations & Applications of Derivatives

### About This Chapter

## Calculations & Applications of Derivatives - Chapter Summary

In this chapter, how to calculate the derivatives of polynomial, exponential and trigonometric functions is explained. How derivatives relate to inverse trigonometric functions is also covered. You will also learn how to apply the rules of differentiation to derivative calculations, including quotient, product and chain rules.

As you continue through the lessons, how to calculate higher order derivatives is presented, as well as how to solve optimization problems in calculus. This chapter will teach you how to:

- Use simple tricks to calculate the derivative of a polynomial equation
- Calculate derivatives of exponential and trigonometric functions
- Solve derivative problems using rules
- Define mathematical jerk
- Tell whether a function is increasing or decreasing by looking at the sign of the first derivative
- Determine min-max problems by using derivatives

Use these lessons and quizzes to gauge how well you understood the material and where you might need further study. If you'd like to review just one part of a video lesson, use the video tabs featured in the Timeline to jump directly to the section you'd like to watch. Each lesson is accompanied by a printable transcript so you can print a copy to review offline at any time. If you have questions about the lesson, contact one of our instructors for assistance.

### 1. Calculating Derivatives of Polynomial Equations

Polynomials can describe just about anything and are especially common in describing motion. Learn the tricks to quickly finding the derivatives of these ubiquitous functions.

### 2. Calculating Derivatives of Exponential Equations

Earth's population is booming! But why is the population increasing so much more drastically than it did many years ago? In this lesson, learn how to calculate the rates of change in exponentials by discovering the rules of derivatives with exponents.

### 3. Calculating Derivatives of Trigonometric Functions

The trigonometric functions show up almost everywhere that you have a repeating pattern. In this lesson, learn how to find the derivatives of the trigonometric functions.

### 4. How to Calculate Derivatives of Inverse Trigonometric Functions

Like a metronome, trigonometric functions are regular. Even predictable. In this lesson, you will learn how to use this predictability to remember the derivative formulas for these common functions.

### 5. Applying the Rules of Differentiation to Calculate Derivatives

In this lesson, we'll review common derivatives and their rules, including the product, quotient and chain rules. We'll also examine how to solve derivative problems through several examples.

### 6. Calculating Higher Order Derivatives

Differentiating functions doesn't have to stop with the first or even second derivative. Learn what a mathematical jerk is as you calculate derivatives of any order in this lesson.

### 7. Using the First Derivative to Identify Increasing & Decreasing Functions

After watching this video lesson, you will learn how you can find out if the function is decreasing or increasing by just looking at the sign of the first derivative.

### 8. Optimization Problems in Calculus: Examples & Explanation

In this lesson, we'll take a step-by-step approach to learning how to use calculus to solve problems where a parameter, such as area or volume, needs to be optimized for a given set of constraints.

### 9. Solving Min-Max Problems Using Derivatives

Max and min problems show up in our daily lives extremely often. In this lesson, we will look at how to use derivatives to find maxima and minima of functions, and in the process solve problems involving maxima and minima.

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### Other Chapters

Other chapters within the NDA Exam Preparation & Study Guide course

- About the NDA Exam
- Algebra Concepts
- Advanced Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Analytic Geometry
- Functions, Limits & Continuity
- Derivative Rules
- Integral Calculus
- Differential Equations & Applications
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Probability Concepts in Math
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- Improving Reading Comprehension
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- Understanding Heat Transfer
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