### What is 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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