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