December 4, 2012

1 / 9

# December 4, 2012 - PowerPoint PPT Presentation

December 4, 2012. AIM : How do we find the derivative of products? Can we find derivatives of derivatives?. Do Now : If f(x) = 2cosx – 3sinx + 4, find f’(x) Find g’(x) if g(x) = . HW2.3a Pg. 126 - 128 #1 – 5 odd, 13, 63, 93, 94, 97. How can we find the derivative of

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' December 4, 2012' - tiana

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

December 4, 2012

AIM: How do we find the derivative of products? Can we find derivatives of derivatives?

Do Now:

If f(x) = 2cosx – 3sinx + 4, find f’(x)

Find g’(x) if g(x) =

HW2.3a Pg. 126 - 128 #1 – 5 odd, 13, 63, 93, 94, 97

The Product Rule

How can we find the derivative of

h(x) = 3x2(5x + 1)?

We can use the Product Rule:

If f and g are differentiable functions, then fg is a differentiable and

(fg)’(x) = f(x)g’(x) + g(x)f’(x)

“The derivative of a product is equal to the first function times the derivative of the second plus the second function times the derivative of the first”

Example 1

Use the product rule to find the derivative of

h(x) = 3x2(5x + 1)

Step 1: Define f(x) and g(x)

Step 2: Find f’(x) and g’(x)

Step 3: Plug into formula: f(x)g’(x) + g(x)f’(x) and simplify

Practice
• Find
• Find if
• Find
What if they’re combined with other derivatives?
• Find f’(x) if f(x) = xsinx
• Find g’(x) if g(x) = excosx
• Find h’(x) if h(x) = sinxcosx
Find the derivatives

Find the derivative of:

Higher Derivatives

Now find the second derivative:

And the third derivative:

Practice
• Find if f(x) = 4x3 – 2x + x-1
• Find f (3)(x) if f(x) = xex