Differentiation Rules - Weebly



At this point you should know the technical definition of a derivative involving the limit of the difference quotient.

[pic]

Now forget everything you learned about limits, because it is time for the differentiation rules!

The Basic Differentiation Rules

▪ The Constant Rule

▪ The Power Rule

▪ The Constant Multiple Rule

▪ The Sum Rule and the Difference Rule

The “Not-So-Basic” Differentiation Rules

▪ The Product Rule

▪ The Quotient Rule

▪ The Chain Rule

Plus

▪ Implicit Differentiation

▪ Higher Order Derivatives

Note

Later in Chapter 7 we will cover

▪ derivatives of trigonometric functions

and in Chapter 8

▪ derivatives of exponential and logarithmic functions.

The Basic Differentiation Rules

1. The Constant Rule

If f(x) = c, then [pic].

Examples

Find [pic] for the given functions.

a) f(x) = 7

b) f(x) = π

2. The Power Rule

If [pic], then [pic].

This rule works for any power: a positive, a negative, or a fraction.

Examples

Find [pic] for the given functions.

a) [pic] e) [pic] (rewrite using with a negative exponent)

b) [pic] f) [pic] (rewrite the radical function as a

power function)

c) [pic]

d) [pic]

3. The Constant Multiple Rule

A coefficient has no effect on the process of differentiation.

If [pic], then [pic].

In Leibniz notation: [pic].

Examples

a) [pic] c) [pic]

b) [pic] d) [pic]

4. The Sum and Difference Rules

If you want the derivative of a sum (or difference) of terms, take the derivative of each

term separately.

Sum

[pic]

Using Leibniz notation: [pic]

Difference

[pic]

Using Leibniz notation: [pic]

Examples

a)

b)

c)

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download