2. The Table of Derivative Rules
•What is a derivative?
•Exponent Rule
•Product Rule
•Chain Rule
•Trig. Rules
•Natural Log
•eˣ
3. What’s a Derivative
Derivative is the instant rate
of change. There are
several rules which make it
easier to find the derivative.
Today we will discover those
rules!
4. Express a Derivative?
A derivative can be
expressed by:
• the lim as x → 0 of dy/dx
• (f(x-Δx) – f(x))/ Δx
• dy/dx
6. Exponent Rule
• The simplest of
the derivative
rules, applied to a
letter such as x to
a specific power.
• xⁿ = nxn-1
• Example:
• x5 = 5x4
7. Product rule applies when deriving two functions
•This
Rule
which are multiplied.
• f(x)g(x) is two functions multiplied
• the derivative is: g(x)f’(x) + f(x)g’(x)
•The process is as follows
• make one function A and the other B; in
this case A is f(x) and B is g(x)
•Then derive each function separately
• then multiply B*A’ and add it to A*B’
8. Quotient Rule
•This rule applies when deriving two functions
which are being divided.
• f(x)/g(x) is an example.
•The derivative is (g(x)f’(x) – f(x)g’(x))/((g(x)2)
• the process reach the derivative is as follows
• make one function A and the other B; in this
case A is f(x) and B is g(x)
• derive each function separately
• then multiply B*A’ and A*B’
• then B*A’ – A*B’
• then divide by B2
9. Chain Rule
One of the most important derivative rules, the chain rule applies
when one function is within the other.
For example : f(g(x))
To derive this, by using the chain rule, first derive the f function so in
this case it would be f’g(x)
Then derive the inside function in this case it would be g’(x)
Then multiply the derivatives together making a final answer of f’g(x)
*g’(x)
Pay close attention to the inside equation
as it may include other rules.
10. Trig. Rules The easy stuff! Just
memorize what the
derivative of each function
is and if needed apply the
other rules.
Function Derivative
Sin(x) Cos(x)
Cos(x) -Sin(x)
Tan(x) Sec2(x)
Cot(x) -CSC2(x)
Sec(x) Sec(x)Tan(x)
CSC(x) -CSC(x)Cot(x)
11. New Rules (ln and ex)
• ln(x) the derivative of this is 1/x
• ex the derivative of this is ex
These are mostly
memorization as well,
however you’ll be
surprised that one of
these functions
derivatives is the same
as the function.
