Derivative

A measure for the rate of change for a Function with one input and one output. Derived from the Difference Quotient.

Notations

Leibniz Notation

$\frac{dy}{dx}f(x)$ OR $\frac{d^{n}y}{d{x}^n}f(x)$ OR $\frac{d^n}{d{x}^n}f(x)$ OR ${\lim }_{x\to 0}\frac{△y}{△x}f(x)$ OR $\frac{dy}{dx}{|}_{x=a,y=b}$

Prime

$f^{\prime }(x)$

Concepts

• Differentiability
• Derivative Formal Definition
• Derivative Matrix Definition
• First Principles

Derivation Rules

These are all theorems.

1. The first part declares the new function is differentiable and that individual derivatives exist
2. The second part give the formula to get the corresponding derivative

List

• Difference Quotient
• Derivative of A Constant
• Derivative Power Rule
• Derivative Constant Multiple
• Derivative Sum Difference
• Derivative Product Rule
  • Derivative Triple Product Rule
  • Derivative Quadruple Product Rule
• Derivative Quotient Rule
• Derivative Chain Rule
• Derivative Power of A Function Rule
• Derivative of Exponential with Euler’s Number Base
• Derivative of General Exponential
• Derivative of Natural Logarithm
• Derivative of General Logarithmic Function
• Derivative of Sine Function
• Derivative of Cosine Function
• Derivative of Tangent Function
• Derivative of Cosecant Function
• Derivative of Secant Function
• Derivative of Cotangent Function
• Derivative of Trig Inverse Functions
• Derivative of Inverse Function
• Derivative of Function to a Function Power
• Derivative of Hyperbolic Functions
• Derivative of Inverse Hyperbolic Functions