### Differentiation

Given a function and a specific point, the differentiation at that point is the slope of a tangent line at that point.

If f(x) is the original function, then the differentiation of f is f'(x) (pronounced f prime) or df/dx

The derivative is sometimes called the slope of the tangent line to the graph at a particular point.

The differentation is also commonly called the derivative

#### First Principals

This deriavative is a linear operator that inputs a function and returns another function.

This is in contrast to an algebraic equation that inputs a number and returns another number.

#### Leibniz Notation

dx

#### Straight Lines

y = mx + c

#### Polynomials

A line through 2 points on a curve is called a secant line

example - x squared

derivative is 2x

example - x cubed - x squared + 4x -3

#### Two Functions

#### Derivative of Ln

#### Derivative of Ln with functional argument

#### Rules

Examples

#### Derivative of e

#### Derivative of e with functional argument

The derivative of e with a functional exponent is equal to e with that derivative of that exponent.

We can use the chain rule here because we have a composite function.

Examples

#### Logarithms

#### Rules

Examples

#### Trigonometric

Examples

#### Inverse

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