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Calculus

Definition of derivative - Home
- AP Calculus BC
- Derivatives

Still Confused?

Try reviewing these fundamentals first

Calculus

Definition of derivative Still Confused?

Try reviewing these fundamentals first

Calculus

Definition of derivative Nope, got it.

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Get Started Now- Intro Lesson1:18
- Lesson: 1a3:40
- Lesson: 1b4:27
- Lesson: 1c2:31
- Lesson: 2a2:13
- Lesson: 2b3:00
- Lesson: 2c2:23

Basic Concepts: Definition of derivative

Recall when finding the slope of two points, we use the formula

Since the slope is the derivative, we can actually use this formula to estimate derivatives from a table.

We will just readjust the slope formula to look like this:

$f'(a) \approx \frac{f(a+h) - f(a)}{h}$

Use this when estimating the slope of the very **first** point of the table

$f'(a) \approx \frac{f(a+h) - f(a-h)}{2h}$

Use this when estimating the slope of **middle** points of the table

$f'(a) \approx \frac{f(a) - f(a-h)}{h}$

Use this when estimating the slope of the very **last point** of the table

**Note that we will not use these formulas in the videos. We will just use the simple slope formula.**

- IntroductionEstimating Derivatives from a table Overview:
- 1.
**Estimating Derivatives**Use the table below to estimate the following derivatives as accurately as possible:

a)$f'(1)$b)$f'(3)$c)$f'(5)$ - 2.Use the table below to estimate the following derivatives as accurately as possible:a)$f'(2)$b)$f'(6)$c)$f'(10)$

2.

Derivatives

2.1

Definition of derivative

2.2

Estimating derivatives from a table

2.3

Power rule

2.4

Chain rule

2.5

Derivative of trigonometric functions

2.6

Derivative of exponential functions

2.7

Derivative of logarithmic functions

2.8

Product rule

2.9

Quotient rule

2.10

Derivative of inverse trigonometric functions

2.11

Implicit differentiation

2.12

Higher order derivatives