3.3 Rules for Differentiation Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer Powers of x Second and Higher Order Derivatives

Derivative of a Constant The notation in your book might look different from what you learned before, but you should be able to switch back and forth between notations.

Positive Integer Powers, Multiples

Sums and differences

The Product Rule

Try these:

The Quotient Rule

Try this:

Negative integer powers of x

Higher order derivatives For the second derivative of y: When finding the “n th ” derivative, we use the notation:

Example 9: Finding Instantaneous Rates of Change An orange farmer currently has 200 trees yielding an average of 15 bushels of oranges per tree. She is expanding her farm at the rate of 15 trees per year, while improved husbandry is improving her average annual yield by 1.2 bushels per tree. What is the current (instantaneous) rate of increase of her total annual production of oranges?

The function f is differentiable for all real numbers. Estimate the following: x02468 f(x)96534

Derivatives from Numerical Data:

Assignment 3.3A: p.124:1,5,13,17,21,29,32,52,56 and p. 126: Quick Quiz: 1,2 3.3B: p. 124: 7,23,27,38,41,46,49,51; Read Section 3.4