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Applied Calculus (MAT 121) Dr. Day Thursday Feb 2, 2012PowerPoint Presentation

Applied Calculus (MAT 121) Dr. Day Thursday Feb 2, 2012

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Applied Calculus (MAT 121)Dr. Day Thursday Feb 2, 2012 Derivatives of Products and Quotients (3.2) Assignments & Test #1 Results

Review

- Meaning and Definition of the Derivative (2.6)
- Shortcut Rules for Determining Derivatives (3.1)
- Applications Requiring Use of Derivatives (2.6, 3.1)

MAT 121

Review: Limits and Derivatives

- What do we mean when we say we are “determining the limit of a function at a point?”
- Show a graphical and a numerical example to illustrate this.
- Write a sentence or two to tie it all together.

- What is our purpose in determining the derivative of a function? Why bother?
- State the formal definition for the derivative of a function f(x).

MAT 121

Applications of Derivatives

MAT 121

Applications of Derivatives

MAT 121

Review: Shortcuts for Determining Derivatives (3.1)

MAT 121

Shortcut Rules for Determining Derivatives (3.1)

- What if the function is a constant function? y = k
- What if the function is a power function? y = xn
- What if the function includes a coefficient? y = cf(x)
- What if the function is the sum or difference of several functions? y = cf(x) + dg(x)
Applications of Derivatives

MAT 121

Shortcut Rules for Derivatives (3.1)

- What if the function is a constant function? y = k
- The derivative of any constant function is 0:
If y = f(x) = k, then y’ = f’(x) = 0

MAT 121

Shortcut Rules for Derivatives (3.1)

- What if the function is a power function? y = xn
If y = f(x) = xn, then y’ = f’(x) = nxn-1.

MAT 121

Shortcut Rules for Derivatives (3.1)

- What if the function includes a coefficient? y=cf(x)
If y = cf(x), then y’ = cf’(x).

MAT 121

Shortcut Rules for Derivatives (3.1)

- What if the function is the sum or difference of several functions? y=cf(x) + dg(x)
If y = cf(x) + dg(x), then y’ = cf’(x) + dg’(x).

MAT 121

Derivatives of Products (3.2)

If y = h(x) = f(x)g(x), then

y’ = h’(x) = f’(x)g(x) + f(x)g’(x)

The derivative of a product of two functions is:

The derivative of the first times the second

plus

the first times the derivative of the second.

MAT 121

Derivatives of Quotients (3.2)

If:

Then:

The derivative of a quotient of two functions is:

The derivative of the top times the bottom

minus

the top times the derivative of the bottom

All over

The bottom squared.

MAT 121

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