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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

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December 4 2012

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
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
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
Practice

  • Find

  • Find if

  • Find


What if they re combined with other derivatives
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 derivatives

Find the derivative of:


Higher derivatives
Higher Derivatives

Now find the second derivative:

And the third derivative:


Practice1
Practice

  • Find if f(x) = 4x3 – 2x + x-1

  • Find f (3)(x) if f(x) = xex