Theorems+on+Differentiation+(power,+chain,+etc.)

=__﻿Rules for Differentiation__= There are many rules that allow derivatives to be found more quickly and easily.

1. Derivative of a Constant
The derivative of a constant is always equal to Zero. For example, the derivative of f(x)=3 is 0

2. Power Rule
To find the derivative of x n, multiply by n and subtract 1 from the exponent. If f(//x//)=//x// 2, then f '(//x//)=2//x//

3. Constant Multiple Rule
If a differentiable function is multiplied by a constant, then its derivative is multiplied by that constant.

u is a differentiable function with respect to //x//, and //c// is any constant. If f(//x//)=3//x// 2, then f '(//x//)=3 x 2//x//=6//x//

4. Sum and Difference Rule
To differentiate polynomials, we can can add or subtract the derivatives of the monomials that make up the polynomial. for functions //u// and //v// that are differentiable with respect to //x// If f(//x//)=//x// 2 +3//x//+2, then f '(//x//)=2//x//+3+0=2//x//+3

5. Product Rule
For functions that are the product of two functions, their derivatives are the sum of the products: In other words, "One prime-Two plus Two prime-One"
 * 1**. the first function and the second's derivative and **2**. the second function with the first's derivative.

6. Quotient Rule
The derivative of a quotient of two functions also has a special rule For Example: