Tags » Derivatives

How To: Implicit Differentiation

IMPLICIT DIFFERENTIATION

Guidelines for Implicit Differentiation:

  1. Differentiate both sides of the equation with respect to x.
  2. Collect all terms involving dy/dx on one side of the equation and move all other terms to the opposite side of the equation.
  3. 44 more words
Definitions

How To: The Chain Rule

CHAIN RULE

 The Chain Rule is better explained by an example:

f(x) = (4x – 1)^3

f'(x) = 3[(4x - 1)^2](4)

f'(x) = 12(4x – 1)^2… 43 more words

Definitions

How To: Find the tangent line to a function

TANGENT LINE TO A FUNCTION

Example:

Find the tangent line to the function f(x) = (x + 2)^2 at the point (0,4).

First, find the derivative: 37 more words

How-to

How To: Quotient Rule

QUOTIENT RULE

The Quotient Rule states that the derivative of f/g is given by the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

Examples:

Definitions

Derivatives of Trigonometric Functions

The following are the derivatives of trigonometric functions:

Examples:

1) f(x) = 2sinx

f'(x) = 2cosx

Examples

How To: Differentiation & Power Rule

DIFFERENTIATION

The derivative of a function is the slope of that function; if it is a curve, the derivative is the tangent line to that function. 94 more words

Definitions