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)
................
................
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