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Section 3.3 The Product and Quotient Rule. Consider the function –What is its derivative? –What...
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Section 3.3 The Product and Quotient Rule
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Transcript of Section 3.3 The Product and Quotient Rule. Consider the function –What is its derivative? –What...
Section 3.3The Product and Quotient Rule
• Consider the function– What is its derivative?– What if we rewrite it as a product– Now what is the derivative?
• So if f and g are differentiable functions we have (fg)’ ≠ f ’g’
• Thus we come to another rule
6xy
42 xxy
Theorem 3.3: Product Rule
• If u = f(x) and v = g(x) are differentiable, then
(fg)’ = f ’g + f g’• The product rule can also be written
• “The derivative of the product is the derivative of the first times the second plus the derivative of the second times the first”
dx
dvuv
dx
du
dx
uvd
)(
Examples
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• Just like with products, we have a similar rule for quotients
• In fact we can derive the rule from our product rule
Section 3.4: Quotient Rule
• If u = f(x) and v = g(x) are differentiable, then
• The quotient rule can also be written
2
/''
g
fggf
g
f
2vdxdv
uvdxdu
v
u
dx
d
Examples
3
2
3
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x
