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# 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

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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

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

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”

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

• Find

• Find if

• Find

• Find f’(x) if f(x) = xsinx

• Find g’(x) if g(x) = excosx

• Find h’(x) if h(x) = sinxcosx

Find the derivative of:

Now find the second derivative:

And the third derivative:

• Find if f(x) = 4x3 – 2x + x-1

• Find f (3)(x) if f(x) = xex