Lesson 2.3Product & Quotient Rules
and Higher Derivatives
Product Rule
If a function is the product of 2 functions, the derivative is:
1st ● (derivative of 2nd) + 2nd ● (derivative of 1st)
Example
Quotient Rule
If a function is the quotient of 2 functions, the derivative is:
[bottom ● (derivative of top) − top ● (derivative of bottom)] ÷ bottom2
Mathematical Proofs: The Product Rule
xgxfdxd
Example
Example
More Trig Derivatives
xdxd tan
Draw the position of a ball rolling off a table:
Now try to draw a graph of the velocity of the ball:
Finally, graph the acceleration of the ball:
Higher Order Derivatives
s(t) position
v(t) = s’(t) velocity
a(t) = v’(t) = s’’(t) acceleration
Example
Problem Set 2.3
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