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

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applied calculus mat 121 dr day thursday feb 2 2012
Applied Calculus (MAT 121)Dr. Day Thursday Feb 2, 2012

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)
  • Derivatives of Products and Quotients (3.2)
  • Assignments & Test #1 Results

MAT 121

review limits and derivatives
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

shortcut rules for determining derivatives 3 1
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 = cf(x)
  • What if the function is the sum or difference of several functions? y = cf(x) + dg(x)

Applications of Derivatives

MAT 121

shortcut rules for derivatives 3 1
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 11
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 12
Shortcut Rules for Derivatives (3.1)
  • What if the function includes a coefficient? y=cf(x)

If y = cf(x), then y’ = cf’(x).

MAT 121

shortcut rules for derivatives 3 13
Shortcut Rules for Derivatives (3.1)
  • What if the function is the sum or difference of several functions? y=cf(x) + dg(x)

If y = cf(x) + dg(x), then y’ = cf’(x) + dg’(x).

MAT 121

derivatives of products 3 2
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
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

assignments
Assignments

WebAssign

  • 3.1 tonight
  • 3.2 Friday night

MAT 121

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