Ch 9: Calculating Derivatives and Derivative Rules in AP Calculus: Homework Help Resource

1. Using Limits to Calculate the Derivative

Limits provide a way to identify the derivative in calculations and graphs. See how both constant and non-constant derivatives are calculated using limits, and how this translates from the equations to a graph.

2. The Linear Properties of a Derivative

Learning about the linear properties of a derivative in mathematics using the constant and distribute rules can broaden your maths repertoire. Read more about these mathematics functions and look at further examples.

3. Calculating Derivatives of Trigonometric Functions

The relationships between location and movement are modeled using trigonometric functions. Learn how to calculate the derivatives of and graph the primary trigonometric functions.

4. Calculating Derivatives of Polynomial Equations

Derivatives of polynomial functions can be solved in a simpler way by using the power rule for derivates. See how this rule can be used to solve vertical velocity functions, and how to find derivatives of polynomials through examples of the steps involved.

5. Calculating Derivatives of Exponential Equations

The derivatives of exponential equations are used to predict rates of change, and can be calculated using exponential equations. Understand the rules of derivatives when used in exponential equations through two examples of differing complexity.

6. Using the Chain Rule to Differentiate Complex Functions

The chain rule can be useful to connect different sections of equations together to differentiate the parts of nested equations. See examples of how the chain rule can help solve trig functions, and those without paratheses.

7. Differentiating Factored Polynomials: Product Rule and Expansion

The product rule is for differentiating products of functions. Learn more about the product rule, and see some examples of solving using the product rule and finding the derivative through expansion.

8. When to Use the Quotient Rule for Differentiation

The quotient rule can be used for differentiation when taking the derivative of a function divided by another function. Gain a better understanding of when to use the quotient rule and explore some examples in this lesson.

9. Understanding Higher Order Derivatives Using Graphs

A derivative of a derivative is called a higher-order derivative. Learn about the rate of change of Super C and acceleration as well as the higher order derivatives and second derivatives.

10. Calculating Higher Order Derivatives

Higher order derivatives, 2nd, 3rd, and 4th order derivatives, can be calculated using the change in rate of acceleration, known as 'jerk'. Learn how to find these higher order derivatives and the concept of 'jerk' in mathematics.

11. How to Find Derivatives of Implicit Functions

Implicit functions are those where both variables are expressed on either side of the equation, and can be simplified through a process known as implicit differentiation. See how this process can find derivatives of implicit functions and explore the steps involved.

12. How to Calculate Derivatives of Inverse Trigonometric Functions

A methodology to learn in maths is the functions of the inverse trigonometric function to calculate distances and angles. Learn more about how to calculate derivatives of inverse trigonometric and it's functions.

13. Applying the Rules of Differentiation to Calculate Derivatives

The rules of differentiation are useful to find solutions to standard differential equations. Identify the application of product rule, quotient rule, and chain rule to solving these equations through examples.